Question 1

State the number of solutions of the system of linear equations  {y=3x−7y=7x−3\left\{ \begin{array} { l } y = 3 x - 7 \y = 7 x - 3\end{array} ight.{y=3x−7y=7x−3​  without solving the system.

Accepted Answer

A)  infinitely many solutions
B)  one solution
C)  no solution

Question 2

A fundraising dinner was held on two consecutive nights. On the first night, 160 adult tickets and 237 children's tickets were sold, for a total of $3,478.25. On the second night, 193 adult tickets and 314 children's tickets were sold, for a total of $4,399.5. Find the price of each type of ticket.

Accepted Answer

A)  The adult tickets were $13 and the children's tickets were $7.25.
B)  The adult tickets were $11 and the children's tickets were $6.5.
C)  The adult tickets were $14.25 and the children's tickets were $7.25.
D)  The adult tickets were $11 and the children's tickets were $7.25.
E)  The adult tickets were $14.25 and the children's tickets were $6.5.

Question 3

The sum of the measures of two angles of a triangle is twice the measure of the third angle. The measure of the second angle is 9∘ more than the measure of the third angle. Find the measures of the three angles.

Accepted Answer

A)  The first angle is 60∘ , the second angle is 51∘ , and the third angle is 69∘ .
B)  The first angle is 69∘, the second angle is 60∘ , and the third angle is 51∘.
C)  The first angle is 51∘ , the second angle is 60∘ , and the third angle is  69∘69 ^ { \circ }69∘  .
D)  The first angle is  510510510  , the second angle is  69∘69 ^ { \circ }69∘  , and the third angle is  60∘60 ^ { \circ }60∘  .
E)  The first angle is  69∘69 ^ { \circ }69∘  , the second angle is  510510510  , and the third angle is  60∘60 ^ { \circ }60∘  .

Question 4

Solve the system of linear equations below by the method of elimination.  {12x+13y=193x−4y=−133\left\{ \begin{array} { l } \frac { 1 } { 2 } x + \frac { 1 } { 3 } y = \frac { 1 } { 9 } \\3 x - 4 y = - \frac { 13 } { 3 }\end{array} ight.⎩⎨⎧​21​x+31​y=91​3x−4y=−313​​

Accepted Answer

A)    (13,56) \left( \frac { 1 } { 3 } , \frac { 5 } { 6 } \right) (31​,65​)  
B)    (−23,12) \left( - \frac { 2 } { 3 } , \frac { 1 } { 2 } \right) (−32​,21​)  
C)    (13,−56) \left( \frac { 1 } { 3 } , - \frac { 5 } { 6 } \right) (31​,−65​)  
D)    (−13,56) \left( - \frac { 1 } { 3 } , \frac { 5 } { 6 } \right) (−31​,65​)  
E)    (−43,−13) \left( - \frac { 4 } { 3 } , - \frac { 1 } { 3 } \right) (−34​,−31​)

Question 5

Graph the equations in the system. Use the graphs to determine whether the system is consistent or inconsistent. If the system is consistent, determine the number of solutions.  {5x+y=−8−5x−y=8\left\{ \begin{array} { l } 5 x + y = - 8 \- 5 x - y = 8\end{array} ight.{5x+y=−8−5x−y=8​

Accepted Answer

A)  The system is consistent and there is only one solution. 
B)  The system is inconsistent. 
C)  The system is consistent and there are infinite number of solutions. 
D)  The system is consistent and there is only one solution. 
E)  The system is consistent and there is only one solution.

Question 6

Write the system of linear equations represented by the augmented matrix below. Use variables x , y , z , v , and w. 
 [−4−6−77−9−4−3−3−79−2−1−57−2−7−7−7−73]\left[ \begin{array} { c c c c : c } - 4 & - 6 & - 7 & 7 & - 9 \- 4 & - 3 & - 3 & - 7 & 9 \- 2 & - 1 & - 5 & 7 & - 2 \- 7 & - 7 & - 7 & - 7 & 3\end{array} ight]​−4−4−2−7​−6−3−1−7​−7−3−5−7​7−77−7​−99−23​​

Accepted Answer

A)    {−4x−6y−7z+7w=−9−4x−3y−3z−7w=9−2x−y−5z+7w=−2−7x−7y−7z−7w=3\left\{ \begin{array} { l } - 4 x - 6 y - 7 z + 7 w = - 9 \- 4 x - 3 y - 3 z - 7 w = 9 \- 2 x - y - 5 z + 7 w = - 2 \- 7 x - 7 y - 7 z - 7 w = 3\end{array} ight.⎩⎨⎧​−4x−6y−7z+7w=−9−4x−3y−3z−7w=9−2x−y−5z+7w=−2−7x−7y−7z−7w=3​ 
B)    {−4x−6y−7z+7w=−16−4x−3y−3z−7w=6−2x−y−5z+7w=−7−7x−7y−7z−7w=10\left\{ \begin{array} { l } - 4 x - 6 y - 7 z + 7 w = - 16 \- 4 x - 3 y - 3 z - 7 w = 6 \- 2 x - y - 5 z + 7 w = - 7 \- 7 x - 7 y - 7 z - 7 w = 10\end{array} ight.⎩⎨⎧​−4x−6y−7z+7w=−16−4x−3y−3z−7w=6−2x−y−5z+7w=−7−7x−7y−7z−7w=10​ 
C)    {−4x−6y−7z+7w−9=0−4x−3y−3z−7w+9=0−2x−y−5z+7w−2=0−7x−7y−7z−7w+3=0\left\{ \begin{array} { r } - 4 x - 6 y - 7 z + 7 w - 9 = 0 \- 4 x - 3 y - 3 z - 7 w + 9 = 0 \- 2 x - y - 5 z + 7 w - 2 = 0 \- 7 x - 7 y - 7 z - 7 w + 3 = 0\end{array} ight.⎩⎨⎧​−4x−6y−7z+7w−9=0−4x−3y−3z−7w+9=0−2x−y−5z+7w−2=0−7x−7y−7z−7w+3=0​ 
D)    {−4x−6y−7z=−9−4x−3y−3z=9−2x−y−5z=−2−7x−7y−7z=3\left\{ \begin{array} { l } - 4 x - 6 y - 7 z = - 9 \- 4 x - 3 y - 3 z = 9 \- 2 x - y - 5 z = - 2 \- 7 x - 7 y - 7 z = 3\end{array} ight.⎩⎨⎧​−4x−6y−7z=−9−4x−3y−3z=9−2x−y−5z=−2−7x−7y−7z=3​ 
E)    {−4x−6y−7z+7w=0−4x−3y−3z−7w=0−2x−y−5z+7w=0−7x−7y−7z−7w=0\left\{ \begin{array} { r } - 4 x - 6 y - 7 z + 7 w = 0 \- 4 x - 3 y - 3 z - 7 w = 0 \- 2 x - y - 5 z + 7 w = 0 \- 7 x - 7 y - 7 z - 7 w = 0\end{array} ight.⎩⎨⎧​−4x−6y−7z+7w=0−4x−3y−3z−7w=0−2x−y−5z+7w=0−7x−7y−7z−7w=0​

Question 7

Graph the system of linear inequalities below.  {y≥−2y<2\left\{ \begin{array} { l } y \geq - 2 \y < 2\end{array} ight.{y≥−2y<2​

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 8

How many liters of a 34% alcohol solution must be mixed with 84% solution to obtain 16 liters of a 71.5% solution?

Accepted Answer

A)  2 liters of a 34% alcohol solution and 14 liters of 84% alcohol solution is required.
B)  10 liters of a 34% alcohol solution and 6 liters of 84% alcohol solution is required.
C)  12 liters of a 34% alcohol solution and 4 liters of 84% alcohol solution is required.
D)  4 liters of a 34% alcohol solution and 12 liters of 84% alcohol solution is required.
E)  6 liters of a 34% alcohol solution and 10 liters of 84% alcohol solution is required.

Question 9

Match the system of linear inequalities below with its graph. - 1 \x \leq 0\end{array} ight.">{y−1x≤0\left\{ \begin{array} { l } y < x \y > - 1 \x \leq 0\end{array} ight.⎩⎨⎧y−1x≤0

Accepted Answer

A)    - 1 \ x \leq 0 \end{array} ight.  
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B)     
C)     
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B)    - 1 \ x \leq 0 \end{array} ight.  
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C)     
D)     
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C)    - 1 \ x \leq 0 \end{array} ight.  
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B)     
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D)    - 1 \ x \leq 0 \end{array} ight.  
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E)    - 1 \ x \leq 0 \end{array} ight.  
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Question 10

Use back-substitution to solve the system of linear equations below.  {x−y−z=32y−z=−12z=−2\left\{ \begin{aligned}x - y - z & = 3 \2 y - z & = - 12 \z & = - 2\end{aligned} ight.⎩⎨⎧​x−y−z2y−zz​=3=−12=−2​

Accepted Answer

A)    (6,7,2) ( 6,7,2 ) (6,7,2)  
B)    (6,−7,−2) ( 6 , - 7 , - 2 ) (6,−7,−2)  
C)    (−7,6,−2) ( - 7,6 , - 2 ) (−7,6,−2)  
D)    (7,6,2) ( 7,6,2 ) (7,6,2)  
E)    (−6,−7,−2) ( - 6 , - 7 , - 2 ) (−6,−7,−2)

Question 11

Graph the system of linear inequalities below.  {x+y≤2x−2y≥0y≥−1\left\{ \begin{array} { l } x + y \leq 2 \x - 2 y \geq 0 \y \geq - 1\end{array} ight.⎩⎨⎧​x+y≤2x−2y≥0y≥−1​

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 12

Use the graphical method to solve the system of equations below.  {y=x+2y=−x+4\left\{ \begin{array} { l } y = x + 2 \y = - x + 4\end{array} ight.{y=x+2y=−x+4​

Accepted Answer

A)   (1,3)  
B)   (2,2.5)  
C)   (2.3 ,2.5) 
D)   (2.5 ,2.5) 
E)   (1,3)

Question 13

Form the augmented matrix for the system of linear equations below.  {6x+y+z=24x+4y+4z=98x+y+4z=−7\left\{ \begin{array} { r } 6 x + y + z = 2 \4 x + 4 y + 4 z = 9 \8 x + y + 4 z = - 7\end{array} ight.⎩⎨⎧​6x+y+z=24x+4y+4z=98x+y+4z=−7​

Accepted Answer

A)    [29−7]\left[ \begin{array} { c } 2 \9 \- 7\end{array} ight]H403z M403 1759 V0 H319 V1759 v0 v1759 h84z'/>​29−7​M347 1759 V0 H263 V1759 v0 v1759 h84z'/>​ 
B)    [648141144]\left[ \begin{array} { l l l } 6 & 4 & 8 \1 & 4 & 1 \1 & 4 & 4\end{array} ight]H403z M403 1759 V0 H319 V1759 v0 v1759 h84z'/>​611​444​814​M347 1759 V0 H263 V1759 v0 v1759 h84z'/>​ 
C)    [61124449814−7]\left[ \begin{array} { c c c c } 6 & 1 & 1 & 2 \4 & 4 & 4 & 9 \8 & 1 & 4 & - 7\end{array} ight]H403z M403 1759 V0 H319 V1759 v0 v1759 h84z'/>​648​141​144​29−7​M347 1759 V0 H263 V1759 v0 v1759 h84z'/>​ 
D)    [611444814]\left[ \begin{array} { l l l } 6 & 1 & 1 \4 & 4 & 4 \8 & 1 & 4\end{array} ight]H403z M403 1759 V0 H319 V1759 v0 v1759 h84z'/>​648​141​144​M347 1759 V0 H263 V1759 v0 v1759 h84z'/>​ 
E)    [64814114429−7]\left[ \begin{array} { c c c } 6 & 4 & 8 \1 & 4 & 1 \1 & 4 & 4 \2 & 9 & - 7\end{array} ight]H403z M403 1759 V0 H319 V1759 v1200 v1759 h84z'/>​6112​4449​814−7​M347 1759 V0 H263 V1759 v1200 v1759 h84z'/>​

Question 14

Graph the system of linear inequalities below.  {x≥1x−2y≤23x+2y≥5x+y≤4\left\{ \begin{array} { l } x \geq 1 \x - 2 y \leq 2 \3 x + 2 y \geq 5 \x + y \leq 4\end{array} ight.⎩⎨⎧​x≥1x−2y≤23x+2y≥5x+y≤4​

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 15

Find the position equation  s=12at2+v0t+s0s = \frac { 1 } { 2 } a t ^ { 2 } + v _ { 0 } t + s _ { 0 }s=21​at2+v0​t+s0​  for an object that has distance  s=24 feet s = 24 	ext { feet }s=24 feet   at t=1 second,  s=47 feet s = 47 	ext { feet }s=47 feet   at t=2 seconds, and  s=78feets = 78 \mathrm { feet }s=78feet  at  t=3t = 3t=3  seconds.

Accepted Answer

A)    s=9t2+4t+11s = 9 t ^ { 2 } + 4 t + 11s=9t2+4t+11 
B)    s=4t2+11t+9s = 4 t ^ { 2 } + 11 t + 9s=4t2+11t+9 
C)    s=3t2+9t+4s = 3 t ^ { 2 } + 9 t + 4s=3t2+9t+4 
D)    s=11t2+4t+9s = 11 t ^ { 2 } + 4 t + 9s=11t2+4t+9 
E)    s=4t2+3t+11s = 4 t ^ { 2 } + 3 t + 11s=4t2+3t+11

Question 16

Solve the system of linear equations below by any convenient method.  {2x−2y=2−2x+y=−2\left\{ \begin{array} { c } 2 x - 2 y = 2 \- 2 x + y = - 2\end{array} ight.{2x−2y=2−2x+y=−2​

Accepted Answer

A)   (-2,-1) 
B)   (-1,0) 
C)   (1,0) 
D)   (3,-1) 
E)   (2,1)

Question 17

Evaluate the determinant of the matrix. Expand by minors along the row or column that appears to make the computation easiest. Round your answer to three decimals places. 
 [0.30.4−0.3−0.40.2−0.4−0.70.2−0.1]\left[ \begin{array} { c c c } 0.3 & 0.4 & - 0.3 \- 0.4 & 0.2 & - 0.4 \- 0.7 & 0.2 & - 0.1\end{array} ight]​0.3−0.4−0.7​0.40.20.2​−0.3−0.4−0.1​​

Accepted Answer

A)   0.117
B)   0.096
C)   0.25
D)   0.072
E)    0.075

Question 18

Which of the following systems of equations below has the solution (1,4)  ? 
 {4x−6y=−203x−5y=−17,{4x−6y=243x−5y=19,{4x−6y=163x−5y=12,{4x−6y=363x−5y=29,{4x−6y=263x−5y=21\left\{ \begin{array} { l } 4 x - 6 y = - 20 \3 x - 5 y = - 17\end{array} , \left\{ \begin{array} { l } 4 x - 6 y = 24 \3 x - 5 y = 19\end{array} , \left\{ \begin{array} { l } 4 x - 6 y = 16 \3 x - 5 y = 12\end{array} , \left\{ \begin{array} { l } 4 x - 6 y = 36 \3 x - 5 y = 29\end{array} , \left\{ \begin{array} { l } 4 x - 6 y = 26 \3 x - 5 y = 21\end{array} ight. ight. ight. ight. ight.{4x−6y=−203x−5y=−17​,{4x−6y=243x−5y=19​,{4x−6y=163x−5y=12​,{4x−6y=363x−5y=29​,{4x−6y=263x−5y=21​

Accepted Answer

A)    {4x−6y=363x−5y=29\left\{ \begin{array} { l } 4 x - 6 y = 36 \3 x - 5 y = 29\end{array} ight.{4x−6y=363x−5y=29​ 
B)    {4x−6y=263x−5y=21\left\{ \begin{array} { l } 4 x - 6 y = 26 \3 x - 5 y = 21\end{array} ight.{4x−6y=263x−5y=21​ 
C)    {4x−6y=243x−5y=19\left\{ \begin{array} { l } 4 x - 6 y = 24 \3 x - 5 y = 19\end{array} ight.{4x−6y=243x−5y=19​ 
D)    {4x−6y=−203x−5y=−17\left\{ \begin{array} { l } 4 x - 6 y = - 20 \3 x - 5 y = - 17\end{array} ight.{4x−6y=−203x−5y=−17​ 
E)    {4x−6y=163x−5y=12\left\{ \begin{array} { l } 4 x - 6 y = 16 \3 x - 5 y = 12\end{array} ight.{4x−6y=163x−5y=12​

Question 19

Use Cramer s Rule to solve the system of linear equations below.  {−2x+4y=18x+2y=11\left\{ \begin{array} { l } - 2 x + 4 y = 18 \x + 2 y = 11\end{array} ight.{−2x+4y=18x+2y=11​

Accepted Answer

A)   (-2,-2) 
B)   (-2,3) 
C)   (0,4) 
D)   (3,-1) 
E)   (1,5)

Question 20

Solve the system of linear equations below by the method of elimination.  {56b−1112m=−1118−12b+34m=23\left\{ \begin{array} { c } \frac { 5 } { 6 } b - \frac { 11 } { 12 } m = - \frac { 11 } { 18 } \\- \frac { 1 } { 2 } b + \frac { 3 } { 4 } m = \frac { 2 } { 3 }\end{array} ight.⎩⎨⎧​65​b−1211​m=−1811​−21​b+43​m=32​​

Accepted Answer

A)    b=−14 and m=74b = - \frac { 1 } { 4 } 	ext { and } m = \frac { 7 } { 4 }b=−41​ and m=47​ 
B)    b=1112 and m=32b = \frac { 11 } { 12 } 	ext { and } m = \frac { 3 } { 2 }b=1211​ and m=23​ 
C)    b=−112 and m=13b = - \frac { 1 } { 12 } 	ext { and } m = \frac { 1 } { 3 }b=−121​ and m=31​ 
D)    b=−1112 and m=12b = - \frac { 11 } { 12 } 	ext { and } m = \frac { 1 } { 2 }b=−1211​ and m=21​ 
E)    b=54 and m=−32b = \frac { 5 } { 4 } 	ext { and } m = - \frac { 3 } { 2 }b=45​ and m=−23​

Exam 4: Systems of Equations and Inequalities

Use Cramer s Rule to solve the system of linear equations below. $\left\{ \begin{array} { l } - 2 x + 4 y = 18 \\x + 2 y = 11\end{array} \right.$

Correct Answer
verified

Form the augmented matrix for the system of linear equations below. $\left\{ \begin{array} { r } 6 x + y + z = 2 \\4 x + 4 y + 4 z = 9 \\8 x + y + 4 z = - 7\end{array} \right.$

Correct Answer
verified

Graph the system of linear inequalities below. $\left\{ \begin{array} { l } x \geq 1 \\x - 2 y \leq 2 \\3 x + 2 y \geq 5 \\x + y \leq 4\end{array} \right.$

Correct Answer
verified

Use back-substitution to solve the system of linear equations below. $\left\{ \begin{aligned}x - y - z & = 3 \\2 y - z & = - 12 \\z & = - 2\end{aligned} \right.$

Correct Answer
verified

Graph the system of linear inequalities below. $\left\{ \begin{array} { l } y \geq - 2 \\y < 2\end{array} \right.$

Correct Answer
verified

Match the system of linear inequalities below with its graph. $\left\{ \begin{array} { l } y < x \\y > - 1 \\x \leq 0\end{array} \right.$

Correct Answer
verified

Write the system of linear equations represented by the augmented matrix below. Use variables x , y , z , v , and w. $\left[ \begin{array} { c c c c : c } - 4 & - 6 & - 7 & 7 & - 9 \\- 4 & - 3 & - 3 & - 7 & 9 \\- 2 & - 1 & - 5 & 7 & - 2 \\- 7 & - 7 & - 7 & - 7 & 3\end{array} \right]$

Correct Answer
verified

Use the graphical method to solve the system of equations below. $\left\{ \begin{array} { l } y = x + 2 \\y = - x + 4\end{array} \right.$

Correct Answer
verified

Find the position equation $s = \frac { 1 } { 2 } a t ^ { 2 } + v _ { 0 } t + s _ { 0 }$ for an object that has distance $s = 24 \text { feet }$ at t=1 second, $s = 47 \text { feet }$ at t=2 seconds, and $s = 78 \mathrm { feet }$ at $t = 3$ seconds.

Correct Answer
verified

Evaluate the determinant of the matrix. Expand by minors along the row or column that appears to make the computation easiest. Round your answer to three decimals places. $\left[ \begin{array} { c c c } 0.3 & 0.4 & - 0.3 \\- 0.4 & 0.2 & - 0.4 \\- 0.7 & 0.2 & - 0.1\end{array} \right]$

Correct Answer
verified

How many liters of a 34% alcohol solution must be mixed with 84% solution to obtain 16 liters of a 71.5% solution?

Correct Answer
verified

Solve the system of linear equations below by any convenient method. $\left\{ \begin{array} { c } 2 x - 2 y = 2 \\- 2 x + y = - 2\end{array} \right.$

Correct Answer
verified

The sum of the measures of two angles of a triangle is twice the measure of the third angle. The measure of the second angle is 9^∘ more than the measure of the third angle. Find the measures of the three angles.

Correct Answer
verified

Graph the system of linear inequalities below. $\left\{ \begin{array} { l } x + y \leq 2 \\x - 2 y \geq 0 \\y \geq - 1\end{array} \right.$

Correct Answer
verified

Graph the equations in the system. Use the graphs to determine whether the system is consistent or inconsistent. If the system is consistent, determine the number of solutions. $\left\{ \begin{array} { l } 5 x + y = - 8 \\- 5 x - y = 8\end{array} \right.$

Correct Answer
verified

Solve the system of linear equations below by the method of elimination. $\left\{ \begin{array} { l } \frac { 1 } { 2 } x + \frac { 1 } { 3 } y = \frac { 1 } { 9 } \\\\3 x - 4 y = - \frac { 13 } { 3 }\end{array} \right.$

Correct Answer
verified

State the number of solutions of the system of linear equations $\left\{ \begin{array} { l } y = 3 x - 7 \\y = 7 x - 3\end{array} \right.$ without solving the system.

Correct Answer
verified

Correct Answer
verified

A fundraising dinner was held on two consecutive nights. On the first night, 160 adult tickets and 237 children's tickets were sold, for a total of $3,478.25. On the second night, 193 adult tickets and 314 children's tickets were sold, for a total of $4,399.5. Find the price of each type of ticket.

Correct Answer
verified

Solve the system of linear equations below by the method of elimination. $\left\{ \begin{array} { c } \frac { 5 } { 6 } b - \frac { 11 } { 12 } m = - \frac { 11 } { 18 } \\\\- \frac { 1 } { 2 } b + \frac { 3 } { 4 } m = \frac { 2 } { 3 }\end{array} \right.$

Correct Answer
verified

Exam 4: Systems of Equations and Inequalities

Use Cramer s Rule to solve the system of linear equations below. {−2x+4y=18x+2y=11\left\{ \begin{array} { l } - 2 x + 4 y = 18 \\x + 2 y = 11\end{array} \right.{−2x+4y=18x+2y=11​

Correct AnswerverifiedShow Answer

Form the augmented matrix for the system of linear equations below. {6x+y+z=24x+4y+4z=98x+y+4z=−7\left\{ \begin{array} { r } 6 x + y + z = 2 \\4 x + 4 y + 4 z = 9 \\8 x + y + 4 z = - 7\end{array} \right.⎩⎨⎧​6x+y+z=24x+4y+4z=98x+y+4z=−7​

Correct AnswerverifiedShow Answer

Graph the system of linear inequalities below. {x≥1x−2y≤23x+2y≥5x+y≤4\left\{ \begin{array} { l } x \geq 1 \\x - 2 y \leq 2 \\3 x + 2 y \geq 5 \\x + y \leq 4\end{array} \right.⎩⎨⎧​x≥1x−2y≤23x+2y≥5x+y≤4​

Correct AnswerverifiedShow Answer

Use back-substitution to solve the system of linear equations below. {x−y−z=32y−z=−12z=−2\left\{ \begin{aligned}x - y - z & = 3 \\2 y - z & = - 12 \\z & = - 2\end{aligned} \right.⎩⎨⎧​x−y−z2y−zz​=3=−12=−2​

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Graph the system of linear inequalities below. {y≥−2y<2\left\{ \begin{array} { l } y \geq - 2 \\y < 2\end{array} \right.{y≥−2y<2​

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Match the system of linear inequalities below with its graph. {y<xy>−1x≤0\left\{ \begin{array} { l } y < x \\y > - 1 \\x \leq 0\end{array} \right.⎩⎨⎧​y<xy>−1x≤0​

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Use the graphical method to solve the system of equations below. {y=x+2y=−x+4\left\{ \begin{array} { l } y = x + 2 \\y = - x + 4\end{array} \right.{y=x+2y=−x+4​

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How many liters of a 34% alcohol solution must be mixed with 84% solution to obtain 16 liters of a 71.5% solution?

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Solve the system of linear equations below by any convenient method. {2x−2y=2−2x+y=−2\left\{ \begin{array} { c } 2 x - 2 y = 2 \\- 2 x + y = - 2\end{array} \right.{2x−2y=2−2x+y=−2​

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The sum of the measures of two angles of a triangle is twice the measure of the third angle. The measure of the second angle is 9∘ more than the measure of the third angle. Find the measures of the three angles.

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Graph the system of linear inequalities below. {x+y≤2x−2y≥0y≥−1\left\{ \begin{array} { l } x + y \leq 2 \\x - 2 y \geq 0 \\y \geq - 1\end{array} \right.⎩⎨⎧​x+y≤2x−2y≥0y≥−1​

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Graph the equations in the system. Use the graphs to determine whether the system is consistent or inconsistent. If the system is consistent, determine the number of solutions. {5x+y=−8−5x−y=8\left\{ \begin{array} { l } 5 x + y = - 8 \\- 5 x - y = 8\end{array} \right.{5x+y=−8−5x−y=8​

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Solve the system of linear equations below by the method of elimination. {12x+13y=193x−4y=−133\left\{ \begin{array} { l } \frac { 1 } { 2 } x + \frac { 1 } { 3 } y = \frac { 1 } { 9 } \\\\3 x - 4 y = - \frac { 13 } { 3 }\end{array} \right.⎩⎨⎧​21​x+31​y=91​3x−4y=−313​​

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State the number of solutions of the system of linear equations {y=3x−7y=7x−3\left\{ \begin{array} { l } y = 3 x - 7 \\y = 7 x - 3\end{array} \right.{y=3x−7y=7x−3​ without solving the system.

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A fundraising dinner was held on two consecutive nights. On the first night, 160 adult tickets and 237 children's tickets were sold, for a total of $3,478.25. On the second night, 193 adult tickets and 314 children's tickets were sold, for a total of $4,399.5. Find the price of each type of ticket.

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Use Cramer s Rule to solve the system of linear equations below. $\left\{ \begin{array} { l } - 2 x + 4 y = 18 \\x + 2 y = 11\end{array} \right.$

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Form the augmented matrix for the system of linear equations below. $\left\{ \begin{array} { r } 6 x + y + z = 2 \\4 x + 4 y + 4 z = 9 \\8 x + y + 4 z = - 7\end{array} \right.$

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Graph the system of linear inequalities below. $\left\{ \begin{array} { l } x \geq 1 \\x - 2 y \leq 2 \\3 x + 2 y \geq 5 \\x + y \leq 4\end{array} \right.$

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Use back-substitution to solve the system of linear equations below. $\left\{ \begin{aligned}x - y - z & = 3 \\2 y - z & = - 12 \\z & = - 2\end{aligned} \right.$

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Graph the system of linear inequalities below. $\left\{ \begin{array} { l } y \geq - 2 \\y < 2\end{array} \right.$

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Match the system of linear inequalities below with its graph. $\left\{ \begin{array} { l } y < x \\y > - 1 \\x \leq 0\end{array} \right.$

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Use the graphical method to solve the system of equations below. $\left\{ \begin{array} { l } y = x + 2 \\y = - x + 4\end{array} \right.$

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Solve the system of linear equations below by any convenient method. $\left\{ \begin{array} { c } 2 x - 2 y = 2 \\- 2 x + y = - 2\end{array} \right.$

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The sum of the measures of two angles of a triangle is twice the measure of the third angle. The measure of the second angle is 9^∘ more than the measure of the third angle. Find the measures of the three angles.

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Graph the system of linear inequalities below. $\left\{ \begin{array} { l } x + y \leq 2 \\x - 2 y \geq 0 \\y \geq - 1\end{array} \right.$

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Graph the equations in the system. Use the graphs to determine whether the system is consistent or inconsistent. If the system is consistent, determine the number of solutions. $\left\{ \begin{array} { l } 5 x + y = - 8 \\- 5 x - y = 8\end{array} \right.$

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Solve the system of linear equations below by the method of elimination. $\left\{ \begin{array} { l } \frac { 1 } { 2 } x + \frac { 1 } { 3 } y = \frac { 1 } { 9 } \\\\3 x - 4 y = - \frac { 13 } { 3 }\end{array} \right.$

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State the number of solutions of the system of linear equations $\left\{ \begin{array} { l } y = 3 x - 7 \\y = 7 x - 3\end{array} \right.$ without solving the system.

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