Question 1

Solve for x.
-$$\left| \begin{array} { r r r } 
x & - 4 & - 1 \
- 2 & 2 & 0 \
- 1 & - 2 & 8
\end{array} \right| = 10$$

Accepted Answer

The answer of Solve for x.
-\[\left| \begin{array} { r r...

Question 2

Write the system of equations associated with the augmented matrix. Do not solve.
-$$\left[ \begin{array} { r r r | r } 
1 & 0 & 0 & - 8 \
0 & 1 & 0 & - 6 \
0 & 0 & 1 & - 10
\end{array} \right]$$

Accepted Answer

A) $\left\{ \begin{array} { l } x = 0 \ y = - 14 \ z = - 18 \end{array} \right.$ 
B)  $\left\{ \begin{array} { l } x = 15 \ y = 1 \ z = 0 \end{array} \right.$ 
C)  $\left\{ \begin{array} { l } x = - 9 \ y = 5 \ z = 6 \end{array} \right.$ 
D)  $\left\{ \begin{array} { l } x = - 8 \ y = - 6 \ z = - 10 \end{array} \right.$ 
A) $\left\{ \begin{array} { l } x = 0 \ y = - 14 \ z = - 18 \end{array} \right.$ 
B)  $\left\{ \begin{array} { l } x = 15 \ y = 1 \ z = 0 \end{array} \right.$ 
C)  $\left\{ \begin{array} { l } x = - 9 \ y = 5 \ z = 6 \end{array} \right.$ 
D)  $\left\{ \begin{array} { l } x = - 8 \ y = - 6 \ z = - 10 \end{array} \right.$

Question 3

Graph the inequality.
-$x^{2}+y^{2} \leq 1$
 
 A)

Accepted Answer

B)

C) 
  
D) 
  
B)

C) 
  
D)

Question 4

Solve the system using the inverse method.
-$$\left\{ \begin{array} { l } 
x + 2 y + 3 z = 10 \
x + y + z = 2 \
x - 2 z = - 1
\end{array} \right.$$

Accepted Answer

A)  x = -11, y = 18, z = -5 
B)  x = 27, y = 38, z = 13 
C)  x = 10, y = 0, z = 0 
D)  x = -13, y = 28, z = -5 
A)  x = -11, y = 18, z = -5 
B)  x = 27, y = 38, z = 13 
C)  x = 10, y = 0, z = 0 
D)  x = -13, y = 28, z = -5

Question 5

Solve the system of equations using substitution.
-$$\left\{ \begin{array} { l } 
y = x ^ { 2 } - 12 x + 36 \
x + y = 18
\end{array} \right.$$

Accepted Answer

A)  x = 2, y = 16; x = 9, y = 9 
B)  x = 6, y = 12 
C)  x = 2, y = 20; x = 9, y = 9 
D)  x = -2, y = 20; x = -9, y = 27 
A)  x = 2, y = 16; x = 9, y = 9 
B)  x = 6, y = 12 
C)  x = 2, y = 20; x = 9, y = 9 
D)  x = -2, y = 20; x = -9, y = 27

Question 6

Which method should be used to solve the system? Explain your answer, including a description of the first step.
-$$\begin{aligned}
- 3 x ^ { 2 } - y ^ { 2 } & = 4 \
- 10 x ^ { 2 } + 3 y ^ { 2 } & = 64
\end{aligned}$$

Accepted Answer

Either method may be used. Elimination m

Question 7

Find the inverse of the matrix.
-$$\left[ \begin{array} { l l l } 
1 & 3 & 2 \
1 & 3 & 3 \
2 & 7 & 8
\end{array} \right]$$

Accepted Answer

A)  $\left[ \begin{array} { l l l } 1 & \frac { 1 } { 3 } & \frac { 1 } { 2 } \ 1 & \frac { 1 } { 3 } & \frac { 1 } { 3 } \ \frac { 1 } { 2 } & \frac { 1 } { 7 } & \frac { 1 } { 8 } \end{array} \right]$

В) $\left[ \begin{array} { l l l } - 1 & - 3 & - 2 \ - 1 & - 3 & - 3 \ - 2 & - 7 & - 8 \end{array} \right]$ 
C)  $\left[ \begin{array} { r r r } - 3 & 10 & - 3 \ 2 & - 4 & 1 \ - 1 & 1 & 0 \end{array} \right]$ 
D)  No inverse 
A)  $\left[ \begin{array} { l l l } 1 & \frac { 1 } { 3 } & \frac { 1 } { 2 } \ 1 & \frac { 1 } { 3 } & \frac { 1 } { 3 } \ \frac { 1 } { 2 } & \frac { 1 } { 7 } & \frac { 1 } { 8 } \end{array} \right]$

В) $\left[ \begin{array} { l l l } - 1 & - 3 & - 2 \ - 1 & - 3 & - 3 \ - 2 & - 7 & - 8 \end{array} \right]$ 
C)  $\left[ \begin{array} { r r r } - 3 & 10 & - 3 \ 2 & - 4 & 1 \ - 1 & 1 & 0 \end{array} \right]$ 
D)  No inverse

Question 8

Solve the system of equations.
-$$\left\{ \begin{aligned}
x - y + 4 z & = 2 \
5 x + z & = 0 \
x + 2 y + z & = - 4
\end{aligned} \right.$$

Accepted Answer

A)  $x = 0 , y = 0 , z = - 2$ 
B)  Inconsistent, $\varnothing$ 
C)  $x = 0 , y = - 2 , z = 2$ 
D)  $x = 0 , y = - 2 , z = 0$ 
A)  $x = 0 , y = 0 , z = - 2$ 
B)  Inconsistent, $\varnothing$ 
C)  $x = 0 , y = - 2 , z = 2$ 
D)  $x = 0 , y = - 2 , z = 0$

Question 9

Verify that the values of the variables listed are solutions of the system of equations.
-$$\left\{ \begin{array} { r } 
x - y + 4 z = - 3 \
3 x + z = - 2 \
x + 2 y + z = - 12 \
x = 0 , y = - 5 , z = - 2
\end{array} \right.$$

Accepted Answer

A)  solution 
B)  not a solution 
A)  solution 
B)  not a solution

Question 10

Find the value of the determinant.
-$$\left| \begin{array} { r r } 
12 & - 7 \
- 4 & 3
\end{array} \right|$$

Accepted Answer

A)  4 
B)  8 
C)  64 
D)  -8 
A)  4 
B)  8 
C)  64 
D)  -8

Question 11

Find the value of the determinant.
-$$\left| \begin{array} { l l l } 
3 & 5 & 5 \
6 & 3 & 2 \
1 & 1 & 5
\end{array} \right|$$

Accepted Answer

A)  -106 
B)  256 
C)  -86 
D)  86 
A)  -106 
B)  256 
C)  -86 
D)  86

Question 12

Solve the problem.
-A tour group split into two groups when waiting in line for food at a fast food counter. The first group bought 8 slices of pizza and 5 soft drinks for $40.29. The second group bought 6 slices of pizza and 7 soft drinks for $
35)71. How much does one slice of pizza cost?

Accepted Answer

A)  $1.94 per slice of pizza 
B)  $2.44 per slice of pizza 
C)  $3.27 per slice of pizza 
D)  $2.77 per slice of pizza 
A)  $1.94 per slice of pizza 
B)  $2.44 per slice of pizza 
C)  $3.27 per slice of pizza 
D)  $2.77 per slice of pizza

Question 13

Perform the row operation(s) on the given augmented matrix.
-$$\begin{array} { l } 
\mathrm { R } _ { 2 } = - 4 \mathrm { r } _ { 1 } \
{ \left[ \begin{array} { l l | l } 
1 & 7 & 10 \
4 & 8 & - 4
\end{array} \right] }
\end{array}$$

Accepted Answer

A)  $\left[ \begin{array} { r r | r } - 4 & - 28 & - 40 \ 0 & - 20 & - 44 \end{array} \right]$ 
B)  $\left[ \begin{array} { r r | r } 1 & 3 & 10 \ 0 & 10 & 18 \end{array} \right]$ 
C)  $\left[ \begin{array} { r r | r } - 4 & - 28 & - 40 \ 4 & 8 & - 4 \end{array} \right]$ 
D)  $\left[ \begin{array} { r r | r } 1 & 7 & 10 \ 0 & - 20 & - 44 \end{array} \right]$ 
A)  $\left[ \begin{array} { r r | r } - 4 & - 28 & - 40 \ 0 & - 20 & - 44 \end{array} \right]$ 
B)  $\left[ \begin{array} { r r | r } 1 & 3 & 10 \ 0 & 10 & 18 \end{array} \right]$ 
C)  $\left[ \begin{array} { r r | r } - 4 & - 28 & - 40 \ 4 & 8 & - 4 \end{array} \right]$ 
D)  $\left[ \begin{array} { r r | r } 1 & 7 & 10 \ 0 & - 20 & - 44 \end{array} \right]$

Question 14

Solve the system of equations.
-$$\left\{ \begin{aligned}
x - y + 3 z & = 10 \
2 x + z & = 4 \
x + 2 y + z & = 8
\end{aligned} \right.$$

Accepted Answer

A)  $x = - 4 , y = 0 , z = 5$ 
B)  $x = - 4 , y = 5 , z = 0$ 
C)  inconsistent (no solution) 
D)  $x = 0 , y = 5 , z = - 4$ 
A)  $x = - 4 , y = 0 , z = 5$ 
B)  $x = - 4 , y = 5 , z = 0$ 
C)  inconsistent (no solution) 
D)  $x = 0 , y = 5 , z = - 4$

Question 15

Which method should be used to solve the system? Explain your answer, including a description of the first step.
-$$\begin{aligned}
9 x ^ { 2 } + 3 y ^ { 2 } & = 81 \
- 8 x ^ { 2 } - 10 y ^ { 2 } & = 9
\end{aligned}$$

Accepted Answer

Elimination should be used since the equ

Solve for x. - $\left| \begin{array} { r r r } x & - 4 & - 1 \\- 2 & 2 & 0 \\- 1 & - 2 & 8\end{array} \right| = 10$

Write the system of equations associated with the augmented matrix. Do not solve. - $\left[ \begin{array} { r r r | r } 1 & 0 & 0 & - 8 \\0 & 1 & 0 & - 6 \\0 & 0 & 1 & - 10\end{array} \right]$

Solve the system using the inverse method. - $\left\{ \begin{array} { l } x + 2 y + 3 z = 10 \\x + y + z = 2 \\x - 2 z = - 1\end{array} \right.$

Solve the system of equations using substitution. - $\left\{ \begin{array} { l } y = x ^ { 2 } - 12 x + 36 \\x + y = 18\end{array} \right.$

Which method should be used to solve the system? Explain your answer, including a description of the first step. - -3- =4 -10+3 =64

Find the inverse of the matrix. - $\left[ \begin{array} { l l l } 1 & 3 & 2 \\1 & 3 & 3 \\2 & 7 & 8\end{array} \right]$

Solve the system of equations. - $\left\{ \begin{aligned}x - y + 4 z & = 2 \\5 x + z & = 0 \\x + 2 y + z & = - 4\end{aligned} \right.$

Verify that the values of the variables listed are solutions of the system of equations. - $\left\{ \begin{array} { r } x - y + 4 z = - 3 \\3 x + z = - 2 \\x + 2 y + z = - 12 \\x = 0 , y = - 5 , z = - 2\end{array} \right.$

Find the value of the determinant. - $\left| \begin{array} { r r } 12 & - 7 \\- 4 & 3\end{array} \right|$

Find the value of the determinant. - $\left| \begin{array} { l l l } 3 & 5 & 5 \\6 & 3 & 2 \\1 & 1 & 5\end{array} \right|$

Solve the problem. -A tour group split into two groups when waiting in line for food at a fast food counter. The first group bought 8 slices of pizza and 5 soft drinks for $40.29. The second group bought 6 slices of pizza and 7 soft drinks for $ 35)71. How much does one slice of pizza cost?

Perform the row operation(s) on the given augmented matrix. - =-4 1 7 10 4 8 -4

Solve the system of equations. - $\left\{ \begin{aligned}x - y + 3 z & = 10 \\2 x + z & = 4 \\x + 2 y + z & = 8\end{aligned} \right.$

Which method should be used to solve the system? Explain your answer, including a description of the first step. - 9+3 =81 -8-10 =9

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Exam 10: Systems of Equations and Inequalities

Solve for x. - ∣x−4−1−220−1−28∣=10\left| \begin{array} { r r r } x & - 4 & - 1 \\- 2 & 2 & 0 \\- 1 & - 2 & 8\end{array} \right| = 10​x−2−1​−42−2​−108​​=10

Write the system of equations associated with the augmented matrix. Do not solve. - [100−8010−6001−10]\left[ \begin{array} { r r r | r } 1 & 0 & 0 & - 8 \\0 & 1 & 0 & - 6 \\0 & 0 & 1 & - 10\end{array} \right]​100​010​001​−8−6−10​​

Graph the inequality. - x2+y2≤1x^{2}+y^{2} \leq 1x2+y2≤1 A) B) C) D)

Solve the system using the inverse method. - {x+2y+3z=10x+y+z=2x−2z=−1\left\{ \begin{array} { l } x + 2 y + 3 z = 10 \\x + y + z = 2 \\x - 2 z = - 1\end{array} \right.⎩⎨⎧​x+2y+3z=10x+y+z=2x−2z=−1​

Solve the system of equations using substitution. - {y=x2−12x+36x+y=18\left\{ \begin{array} { l } y = x ^ { 2 } - 12 x + 36 \\x + y = 18\end{array} \right.{y=x2−12x+36x+y=18​