Question 1

Solve the system using a graphing utility. $\left\{ \begin{array} { l } 
0.05 x - 0.06 y = 1.41 \
0.45 x + 0.60 y = - 0.02
\end{array} \right.$

Accepted Answer

A)  $( 17.8 , - 14.7 )$ 
B)  $( 14.8 , - 11.1 )$ 
C)  $( 17.8 , - 11.1 )$ 
D)  $( 14.8 , - 14.7 )$ 
E)  $( 15.8 , - 10.1 )$ 
A)  $( 17.8 , - 14.7 )$ 
B)  $( 14.8 , - 11.1 )$ 
C)  $( 17.8 , - 11.1 )$ 
D)  $( 14.8 , - 14.7 )$ 
E)  $( 15.8 , - 10.1 )$ B

Question 2

Use Cramer's rule along with a graphing utility to solve the system. $$\left\{ \begin{aligned}
2 A - B - 3 C + 2 D = & - 4 \
A - 2 B + C - 3 D = & 8 \
3 A - 4 B + 2 C - 4 D = & 24 \
2 A + 3 B - C - 2 D = & - 8
\end{aligned} \right.$$

Accepted Answer

A)  $( 4,2,6,0 )$ 
B)  $( 4 , - 2,6,0 )$ 
C)  $( - 4,2 , - 6 , - 2 )$ 
D)  $( 4 , - 2,6,2 )$ 
E)  $\text { The system is inconsistent. }$ 
A)  $( 4,2,6,0 )$ 
B)  $( 4 , - 2,6,0 )$ 
C)  $( - 4,2 , - 6 , - 2 )$ 
D)  $( 4 , - 2,6,2 )$ 
E)  $\text { The system is inconsistent. }$ D

Question 3

Graph the inequality. $5 x - 7 y > 35$

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)    A

Question 4

Find all solutions of the system. $$\left\{ \begin{array} { r } 
x + y + z = 12 \
2 x - y - z = - 5 \
6 x + 2 y + z = 30
\end{array} \right.$$

Accepted Answer

A)  $\left( \frac { 10 } { 3 } , \frac { 16 } { 3 } , \frac { 10 } { 3 } \right)$ 
B)  $\left( 19 , \frac { 10 } { 3 } , \frac { 7 } { 3 } \right)$ 
C)  $\left( \frac { 7 } { 3 } , \frac { 19 } { 3 } , \frac { 10 } { 3 } \right)$ 
D)  $\text { The system is dependent. }$ 
E)  $\text { The system is inconsistent. }$ 
A)  $\left( \frac { 10 } { 3 } , \frac { 16 } { 3 } , \frac { 10 } { 3 } \right)$ 
B)  $\left( 19 , \frac { 10 } { 3 } , \frac { 7 } { 3 } \right)$ 
C)  $\left( \frac { 7 } { 3 } , \frac { 19 } { 3 } , \frac { 10 } { 3 } \right)$ 
D)  $\text { The system is dependent. }$ 
E)  $\text { The system is inconsistent. }$

Question 5

Find all solutions of the system. $$\left\{ \begin{array} { l } 
x + y + z + w = 4 \
x - 2 y - z - w = 6 \
2 x - y + z - w = 5 \
x - y + 2 z - 2 w = - 5
\end{array} \right.$$

Accepted Answer

A)  $( 0 , - 2,4,5 )$ 
B)  $( 5,0 , - 3,2 )$ 
C)  $( - 8,2 , - 5,0 )$ 
D)  $\text { The system is dependent. }$ 
E)  $\text { The system is inconsistent. }$ 
A)  $( 0 , - 2,4,5 )$ 
B)  $( 5,0 , - 3,2 )$ 
C)  $( - 8,2 , - 5,0 )$ 
D)  $\text { The system is dependent. }$ 
E)  $\text { The system is inconsistent. }$

Question 6

Use matrices to solve the system. $$\left\{ \begin{aligned}
5 x + y + 10 z & = 9 \
4 x + 2 y - 10 z & = 84 \
3 x - 4 y & = 11
\end{aligned} \right.$$

Accepted Answer

A)  $( 9,9 , - 4 )$ 
B)  $( 9,4 , - 4 )$ 
C)  $( 4,9 , - 4 )$ 
D)  $( 4,4 , - 9 )$ 
E)  $\text { The system is inconsistent. }$ 
A)  $( 9,9 , - 4 )$ 
B)  $( 9,4 , - 4 )$ 
C)  $( 4,9 , - 4 )$ 
D)  $( 4,4 , - 9 )$ 
E)  $\text { The system is inconsistent. }$

Question 7

Use Cramer's rule to solve the system. $$\left\{ \begin{aligned}
6 x + 4 y - 2 z = & 10 \
2 x - 3 y + 4 z = & 4 \
15 x - 18 z = & - 21
\end{aligned} \right.$$

Accepted Answer

A)  $( 2,1,1 )$ 
B)  $( 1,0,2 )$ 
C)  $( 1,2,1 )$ 
D)  $( 1,2,2 )$ 
E)  $\text { The system is inconsistent. }$ 
A)  $( 2,1,1 )$ 
B)  $( 1,0,2 )$ 
C)  $( 1,2,1 )$ 
D)  $( 1,2,2 )$ 
E)  $\text { The system is inconsistent. }$

Question 8

Find all solutions of the system. $$\left\{ \begin{aligned}
- x + y + z + w & = 12 \
2 y - z - w & = 7 \
2 z + 5 w & = 18 \
11 w & = 44
\end{aligned} \right.$$

Accepted Answer

A)  $( 4,1 , - 5 , - 4 )$ 
B)  $( - 4,5 , - 1,4 )$ 
C)  $( 5 , - 1 , - 4,4 )$ 
D)  $\text { The system is dependent. }$ 
E)  $\text { The system is inconsistent. }$ 
A)  $( 4,1 , - 5 , - 4 )$ 
B)  $( - 4,5 , - 1,4 )$ 
C)  $( 5 , - 1 , - 4,4 )$ 
D)  $\text { The system is dependent. }$ 
E)  $\text { The system is inconsistent. }$

Question 9

Find all solutions of the system. $$\left\{ \begin{aligned}
x + y - 3 z + 2 w & = - 1 \
- 2 x - 2 y + 6 z + w & = - 13 \
- x + 3 y + 3 z + 3 w & = - 20 \
2 x + y - 3 z - w & = 10
\end{aligned} \right.$$

Accepted Answer

A)  $\left( 2 , - \frac { 3 } { 2 } , - \frac { 3 } { 2 } , - 3 \right)$ 
B)  $\left( - 5 , \frac { 3 } { 2 } , - \frac { 5 } { 2 } , 2 \right)$ 
C)  $\left( - \frac { 3 } { 2 } , - 3 , - 4,2 \right)$ 
D)  $\text { The system is dependent. }$ 
E)  $\text { The system is inconsistent. }$ 
A)  $\left( 2 , - \frac { 3 } { 2 } , - \frac { 3 } { 2 } , - 3 \right)$ 
B)  $\left( - 5 , \frac { 3 } { 2 } , - \frac { 5 } { 2 } , 2 \right)$ 
C)  $\left( - \frac { 3 } { 2 } , - 3 , - 4,2 \right)$ 
D)  $\text { The system is dependent. }$ 
E)  $\text { The system is inconsistent. }$

Question 10

Use a graphing utility to compute the matrix product. $$\left( \begin{array} { r r r r } 
- 6 & 9 & - 5 & 1 \
9 & - 1 & - 5 & 2 \
- 5 & - 5 & 9 & - 3 \
1 & 2 & - 3 & 1
\end{array} \right) \left( \begin{array} { r r r r } 
0.2 & 0.4 & 0.6 & 0.8 \
0.4 & 0.8 & 1.4 & 2.2 \
0.6 & 1.4 & 2.8 & 5 \
0.8 & 2.2 & 5 & 10
\end{array} \right)$$

Accepted Answer

A)  $\left( \begin{array} { c c c c } 
0.2 & 0 & 0 & 0 \
0 & 0.2 & 0 & 0 \
0 & 0 & 0.2 & 0 \
0 & 0 & 0 & 0.2
\end{array} \right)$ 
B)  $\left( \begin{array} { c c c c } 
0 & 0 & 0 & 0 \
0.2 & 0.2 & 0 & 0.2 \
0 & 0 & 0 & 0 \
0 & 0 & 0.2 & 0
\end{array} \right)$ 
C)  $\left( \begin{array} { c c c c } 
0.2 & 0.2 & 0.2 & 0.2 \
0 & 0 & 0 & 0 \
0 & 0 & 0 & 0 \
0 & 0 & 0 & 0
\end{array} \right)$ 
D)  $\left( \begin{array} { c c c c } 
0 & 0 & 0 & 0 \
0 & 0.2 & 0 & 0.2 \
0.2 & 0 & 0.2 & 0 \
0 & 0 & 0 & 0
\end{array} \right)$ 
E)  $\left( \begin{array} { c c c c } 
0 & 0 & 0 & 0.2 \
0 & 0 & 0.2 & 0 \
0 & 0.2 & 0 & 0 \
0.2 & 0 & 0 & 0
\end{array} \right)$ 
A)  $\left( \begin{array} { c c c c } 
0.2 & 0 & 0 & 0 \
0 & 0.2 & 0 & 0 \
0 & 0 & 0.2 & 0 \
0 & 0 & 0 & 0.2
\end{array} \right)$ 
B)  $\left( \begin{array} { c c c c } 
0 & 0 & 0 & 0 \
0.2 & 0.2 & 0 & 0.2 \
0 & 0 & 0 & 0 \
0 & 0 & 0.2 & 0
\end{array} \right)$ 
C)  $\left( \begin{array} { c c c c } 
0.2 & 0.2 & 0.2 & 0.2 \
0 & 0 & 0 & 0 \
0 & 0 & 0 & 0 \
0 & 0 & 0 & 0
\end{array} \right)$ 
D)  $\left( \begin{array} { c c c c } 
0 & 0 & 0 & 0 \
0 & 0.2 & 0 & 0.2 \
0.2 & 0 & 0.2 & 0 \
0 & 0 & 0 & 0
\end{array} \right)$ 
E)  $\left( \begin{array} { c c c c } 
0 & 0 & 0 & 0.2 \
0 & 0 & 0.2 & 0 \
0 & 0.2 & 0 & 0 \
0.2 & 0 & 0 & 0
\end{array} \right)$

Question 11

Use the substitution method to find all solutions of the system. $\left\{ \begin{array} { l } 
3 x - 2 y = - 19 \
x + 4 y = - 4
\end{array} \right.$

Accepted Answer

A)  $\left( - 6,3 \frac { 1 } { 2 } \right)$ 
B)  $\left( - 6 , - \frac { 1 } { 9 } \right)$ 
C)  $\left( - 6 , - \frac { 1 } { 3 } \right)$ 
D)  $\left( - 6 , \frac { 1 } { 2 } \right)$ 
E)  $\left( - 6 , - \frac { 2 } { 3 } \right)$ 
A)  $\left( - 6,3 \frac { 1 } { 2 } \right)$ 
B)  $\left( - 6 , - \frac { 1 } { 9 } \right)$ 
C)  $\left( - 6 , - \frac { 1 } { 3 } \right)$ 
D)  $\left( - 6 , \frac { 1 } { 2 } \right)$ 
E)  $\left( - 6 , - \frac { 2 } { 3 } \right)$

Question 12

Evaluate the determinant. $\left| \begin{array} { c c } 
- 4 & - 9 \
- 7 & 3
\end{array} \right|$

Accepted Answer

A)  $75$ 
B)  $- 75$ 
C)  $- 12$ 
D)  $- 63$ 
E)  $- 72$ 
A)  $75$ 
B)  $- 75$ 
C)  $- 12$ 
D)  $- 63$ 
E)  $- 72$

Question 13

Find all solutions of the system. $$\left\{ \begin{array} { l } 
2 x - 3 y + 2 z = 3 \
4 x + 2 y + 3 z = 13 \
5 x + 4 y + 2 z = 16
\end{array} \right.$$

Accepted Answer

A)  $( 1,2 , - 2 )$ 
B)  $( 1 , - 1,2 )$ 
C)  $( 2,1,1 )$ 
D)  $\text { The system is dependent. }$ 
E)  $\text { The system is inconsistent. }$ 
A)  $( 1,2 , - 2 )$ 
B)  $( 1 , - 1,2 )$ 
C)  $( 2,1,1 )$ 
D)  $\text { The system is dependent. }$ 
E)  $\text { The system is inconsistent. }$

Question 14

Which of the following are linear equations in two variables?

Accepted Answer

A)  $y = x$ 
B)  $\frac { 4 } { x } - \frac { 3 } { y } = - 1$ 
C)  $2 w + 8 z = - 4 w + 3$ 
D)  $y = x ^ { 2 }$ 
E)  $2 x - x = 4$ 
A)  $y = x$ 
B)  $\frac { 4 } { x } - \frac { 3 } { y } = - 1$ 
C)  $2 w + 8 z = - 4 w + 3$ 
D)  $y = x ^ { 2 }$ 
E)  $2 x - x = 4$

Question 15

Is $( 5,3 )$ a solution of the following system? $\left\{ \begin{array} { l } 
5 x - 3 y = 16 \
2 x + 3 y = 19
\end{array} \right.$

Accepted Answer

A) True 
 B)False

Question 16

Use a graphing utility to compute the matrix product. $\left( \begin{array} { r r } 
- 38 & 18 \
23 & 8
\end{array} \right)$ $\left( \begin{array} { r r } 
89 & - 19 \
17 & 44
\end{array} \right)$

Accepted Answer

A)  $\left( \begin{array} { r r } 
- 3,076 & 1,514 \
2,173 & - 85
\end{array} \right)$ 
B)  $\left( \begin{array} { r r } 
- 3,076 & 1,514 \
2,220 & - 85
\end{array} \right)$ 
C)  $\left( \begin{array} { r r } 
- 3,076 & 1,514 \
2,183 & - 85
\end{array} \right)$ 
D)  $\left( \begin{array} { r r } 
- 3,076 & 1,487 \
2,183 & - 85
\end{array} \right)$ 
E)  $\left( \begin{array} { r r } 
- 3,087 & 1,514 \
2,183 & - 85
\end{array} \right)$ 
A)  $\left( \begin{array} { r r } 
- 3,076 & 1,514 \
2,173 & - 85
\end{array} \right)$ 
B)  $\left( \begin{array} { r r } 
- 3,076 & 1,514 \
2,220 & - 85
\end{array} \right)$ 
C)  $\left( \begin{array} { r r } 
- 3,076 & 1,514 \
2,183 & - 85
\end{array} \right)$ 
D)  $\left( \begin{array} { r r } 
- 3,076 & 1,487 \
2,183 & - 85
\end{array} \right)$ 
E)  $\left( \begin{array} { r r } 
- 3,087 & 1,514 \
2,183 & - 85
\end{array} \right)$

Question 17

Find the inverse, if it exists. $$A = \left( \begin{array} { c c } 
\frac { 2 } { 9 } & - \frac { 1 } { 13 } \
- 26 & 9
\end{array} \right)$$

Accepted Answer

A)  $A ^ { - 1 } = \left( \begin{array} { c c } 
- 26 & 13 \
- 5 & 9
\end{array} \right)$ 
B)  $A ^ { - 1 } = \left( \begin{array} { c c } 
1 & 9 \
2 & - 1
\end{array} \right)$ 
C)  $A ^ { - 1 } = \left( \begin{array} { l l } 
- 1 & 5 \
- 2 & 1
\end{array} \right)$ 
D)  $A ^ { - 1 } = \left( \begin{array} { c c } 
11 & 6 \
13 & - 8
\end{array} \right)$ 
E)  $\text { The inverse does not exist. }$ 
A)  $A ^ { - 1 } = \left( \begin{array} { c c } 
- 26 & 13 \
- 5 & 9
\end{array} \right)$ 
B)  $A ^ { - 1 } = \left( \begin{array} { c c } 
1 & 9 \
2 & - 1
\end{array} \right)$ 
C)  $A ^ { - 1 } = \left( \begin{array} { l l } 
- 1 & 5 \
- 2 & 1
\end{array} \right)$ 
D)  $A ^ { - 1 } = \left( \begin{array} { c c } 
11 & 6 \
13 & - 8
\end{array} \right)$ 
E)  $\text { The inverse does not exist. }$

Question 18

The matrices A and B are defined as follows: A = $\left( \begin{array} { r r } 
4 & 5 \
- 1 & 6
\end{array} \right)$ , B = $\left( \begin{array} { r r } 
1 & - 1 \
2 & 0
\end{array} \right)$ Carry out the indicated matrix operation.
A + B

Accepted Answer

A)  $\left( \begin{array} { l l } 
5 & 4 \
1 & 6
\end{array} \right)$ 
B)  $\left( \begin{array} { l l } 
1 & 5 \
5 & 6
\end{array} \right)$ 
C)  $\left( \begin{array} { l l } 
5 & 6 \
1 & 4
\end{array} \right)$ 
D)  $\left( \begin{array} { l l } 
5 & 4 \
1 & 7
\end{array} \right)$ 
E)  $\left( \begin{array} { l l } 
5 & 1 \
1 & 5
\end{array} \right)$ 
A)  $\left( \begin{array} { l l } 
5 & 4 \
1 & 6
\end{array} \right)$ 
B)  $\left( \begin{array} { l l } 
1 & 5 \
5 & 6
\end{array} \right)$ 
C)  $\left( \begin{array} { l l } 
5 & 6 \
1 & 4
\end{array} \right)$ 
D)  $\left( \begin{array} { l l } 
5 & 4 \
1 & 7
\end{array} \right)$ 
E)  $\left( \begin{array} { l l } 
5 & 1 \
1 & 5
\end{array} \right)$

Question 19

Evaluate A by expanding it along the second row. $$A = \left| \begin{array} { c c c } 
4 & 8 & 12 \
16 & 20 & 24 \
28 & 32 & 36
\end{array} \right|$$

Accepted Answer

A)  $1$ 
B)  $4$ 
C)  $- 1$ 
D)  $0$ 
E)  $- 2$ 
A)  $1$ 
B)  $4$ 
C)  $- 1$ 
D)  $0$ 
E)  $- 2$

Question 20

The matrices A and B are defined as follows: A = $\left( \begin{array} { r r } 
4 & 5 \
- 1 & 6
\end{array} \right)$ , B = $\left( \begin{array} { r r } 
1 & - 1 \
2 & 0
\end{array} \right)$ Carry out the indicated matrix operation. $A B$

Accepted Answer

A)  $\left( \begin{array} { c c } 
14 & - 4 \
11 & 13
\end{array} \right)$ 
B)  $\left( \begin{array} { c c } 
14 & - 4 \
11 & 1
\end{array} \right)$ 
C)  $\left( \begin{array} { r r } 
4 & - 13 \
11 & 1
\end{array} \right)$ 
D)  $\left( \begin{array} { c c } 
12 & - 4 \
11 & 13
\end{array} \right)$ 
E)  $\text { not defined }$ 
A)  $\left( \begin{array} { c c } 
14 & - 4 \
11 & 13
\end{array} \right)$ 
B)  $\left( \begin{array} { c c } 
14 & - 4 \
11 & 1
\end{array} \right)$ 
C)  $\left( \begin{array} { r r } 
4 & - 13 \
11 & 1
\end{array} \right)$ 
D)  $\left( \begin{array} { c c } 
12 & - 4 \
11 & 13
\end{array} \right)$ 
E)  $\text { not defined }$

Solve the system using a graphing utility. $\left\{ \begin{array} { l } 0.05 x - 0.06 y = 1.41 \\0.45 x + 0.60 y = - 0.02\end{array} \right.$

Use Cramer's rule along with a graphing utility to solve the system. $\left\{ \begin{aligned}2 A - B - 3 C + 2 D = & - 4 \\A - 2 B + C - 3 D = & 8 \\3 A - 4 B + 2 C - 4 D = & 24 \\2 A + 3 B - C - 2 D = & - 8\end{aligned} \right.$

Graph the inequality. $5 x - 7 y > 35$

Find all solutions of the system. $\left\{ \begin{array} { r } x + y + z = 12 \\2 x - y - z = - 5 \\6 x + 2 y + z = 30\end{array} \right.$

Find all solutions of the system. $\left\{ \begin{array} { l } x + y + z + w = 4 \\x - 2 y - z - w = 6 \\2 x - y + z - w = 5 \\x - y + 2 z - 2 w = - 5\end{array} \right.$

Use matrices to solve the system. $\left\{ \begin{aligned}5 x + y + 10 z & = 9 \\4 x + 2 y - 10 z & = 84 \\3 x - 4 y & = 11\end{aligned} \right.$

Use Cramer's rule to solve the system. $\left\{ \begin{aligned}6 x + 4 y - 2 z = & 10 \\2 x - 3 y + 4 z = & 4 \\15 x - 18 z = & - 21\end{aligned} \right.$

Find all solutions of the system. $\left\{ \begin{aligned}- x + y + z + w & = 12 \\2 y - z - w & = 7 \\2 z + 5 w & = 18 \\11 w & = 44\end{aligned} \right.$

Find all solutions of the system. $\left\{ \begin{aligned}x + y - 3 z + 2 w & = - 1 \\- 2 x - 2 y + 6 z + w & = - 13 \\- x + 3 y + 3 z + 3 w & = - 20 \\2 x + y - 3 z - w & = 10\end{aligned} \right.$

Use the substitution method to find all solutions of the system. $\left\{ \begin{array} { l } 3 x - 2 y = - 19 \\x + 4 y = - 4\end{array} \right.$

Evaluate the determinant. $\left| \begin{array} { c c } - 4 & - 9 \\- 7 & 3\end{array} \right|$

Find all solutions of the system. $\left\{ \begin{array} { l } 2 x - 3 y + 2 z = 3 \\4 x + 2 y + 3 z = 13 \\5 x + 4 y + 2 z = 16\end{array} \right.$

Which of the following are linear equations in two variables?

Is $( 5,3 )$ a solution of the following system? $\left\{ \begin{array} { l } 5 x - 3 y = 16 \\2 x + 3 y = 19\end{array} \right.$

Use a graphing utility to compute the matrix product. $\left( \begin{array} { r r } - 38 & 18 \\23 & 8\end{array} \right)$ $\left( \begin{array} { r r } 89 & - 19 \\17 & 44\end{array} \right)$

Find the inverse, if it exists. $A = \left( \begin{array} { c c } \frac { 2 } { 9 } & - \frac { 1 } { 13 } \\- 26 & 9\end{array} \right)$

The matrices A and B are defined as follows: A = $\left( \begin{array} { r r } 4 & 5 \\- 1 & 6\end{array} \right)$ , B = $\left( \begin{array} { r r } 1 & - 1 \\2 & 0\end{array} \right)$ Carry out the indicated matrix operation. A + B

Evaluate A by expanding it along the second row. $A = \left| \begin{array} { c c c } 4 & 8 & 12 \\16 & 20 & 24 \\28 & 32 & 36\end{array} \right|$

The matrices A and B are defined as follows: A = $\left( \begin{array} { r r } 4 & 5 \\- 1 & 6\end{array} \right)$ , B = $\left( \begin{array} { r r } 1 & - 1 \\2 & 0\end{array} \right)$ Carry out the indicated matrix operation. $A B$

Fundamentals

Equations and Inequalities

Functions

Polynomial and Rational Functions Applications to Optimization

Exponential and Logarithmic Functions

An Introduction to Trigonometry Via Right Triangles

The Trigonometric Functions

Graphs of the Trigonometric Functions

Analytical Trigonometry

Additional Topics in Trigonometry

The Conic Sections

Roots of Polynomial Equations

Additional Topics in Algebra

Filters

Exam 11: Systems of Equations

Solve the system using a graphing utility. {0.05x−0.06y=1.410.45x+0.60y=−0.02\left\{ \begin{array} { l } 0.05 x - 0.06 y = 1.41 \\0.45 x + 0.60 y = - 0.02\end{array} \right.{0.05x−0.06y=1.410.45x+0.60y=−0.02​

Graph the inequality. 5x−7y>355 x - 7 y > 355x−7y>35

Find all solutions of the system. {x+y+z=122x−y−z=−56x+2y+z=30\left\{ \begin{array} { r } x + y + z = 12 \\2 x - y - z = - 5 \\6 x + 2 y + z = 30\end{array} \right.⎩⎨⎧​x+y+z=122x−y−z=−56x+2y+z=30​

Find all solutions of the system. {x+y+z+w=4x−2y−z−w=62x−y+z−w=5x−y+2z−2w=−5\left\{ \begin{array} { l } x + y + z + w = 4 \\x - 2 y - z - w = 6 \\2 x - y + z - w = 5 \\x - y + 2 z - 2 w = - 5\end{array} \right.⎩⎨⎧​x+y+z+w=4x−2y−z−w=62x−y+z−w=5x−y+2z−2w=−5​

Use matrices to solve the system. {5x+y+10z=94x+2y−10z=843x−4y=11\left\{ \begin{aligned}5 x + y + 10 z & = 9 \\4 x + 2 y - 10 z & = 84 \\3 x - 4 y & = 11\end{aligned} \right.⎩⎨⎧​5x+y+10z4x+2y−10z3x−4y​=9=84=11​

Use Cramer's rule to solve the system. {6x+4y−2z=102x−3y+4z=415x−18z=−21\left\{ \begin{aligned}6 x + 4 y - 2 z = & 10 \\2 x - 3 y + 4 z = & 4 \\15 x - 18 z = & - 21\end{aligned} \right.⎩⎨⎧​6x+4y−2z=2x−3y+4z=15x−18z=​104−21​

Find all solutions of the system. {−x+y+z+w=122y−z−w=72z+5w=1811w=44\left\{ \begin{aligned}- x + y + z + w & = 12 \\2 y - z - w & = 7 \\2 z + 5 w & = 18 \\11 w & = 44\end{aligned} \right.⎩⎨⎧​−x+y+z+w2y−z−w2z+5w11w​=12=7=18=44​

Use the substitution method to find all solutions of the system. {3x−2y=−19x+4y=−4\left\{ \begin{array} { l } 3 x - 2 y = - 19 \\x + 4 y = - 4\end{array} \right.{3x−2y=−19x+4y=−4​

Evaluate the determinant. ∣−4−9−73∣\left| \begin{array} { c c } - 4 & - 9 \\- 7 & 3\end{array} \right|​−4−7​−93​​

Find all solutions of the system. {2x−3y+2z=34x+2y+3z=135x+4y+2z=16\left\{ \begin{array} { l } 2 x - 3 y + 2 z = 3 \\4 x + 2 y + 3 z = 13 \\5 x + 4 y + 2 z = 16\end{array} \right.⎩⎨⎧​2x−3y+2z=34x+2y+3z=135x+4y+2z=16​

Which of the following are linear equations in two variables?

Is (5,3)( 5,3 )(5,3) a solution of the following system? {5x−3y=162x+3y=19\left\{ \begin{array} { l } 5 x - 3 y = 16 \\2 x + 3 y = 19\end{array} \right.{5x−3y=162x+3y=19​

Use a graphing utility to compute the matrix product. (−3818238)\left( \begin{array} { r r } - 38 & 18 \\23 & 8\end{array} \right)(−3823​188​) (89−191744)\left( \begin{array} { r r } 89 & - 19 \\17 & 44\end{array} \right)(8917​−1944​)

Find the inverse, if it exists. A=(29−113−269)A = \left( \begin{array} { c c } \frac { 2 } { 9 } & - \frac { 1 } { 13 } \\- 26 & 9\end{array} \right)A=(92​−26​−131​9​)

The matrices A and B are defined as follows: A = (45−16)\left( \begin{array} { r r } 4 & 5 \\- 1 & 6\end{array} \right)(4−1​56​) , B = (1−120)\left( \begin{array} { r r } 1 & - 1 \\2 & 0\end{array} \right)(12​−10​) Carry out the indicated matrix operation. A + B

Evaluate A by expanding it along the second row. A=∣4812162024283236∣A = \left| \begin{array} { c c c } 4 & 8 & 12 \\16 & 20 & 24 \\28 & 32 & 36\end{array} \right|A=​41628​82032​122436​​

The matrices A and B are defined as follows: A = (45−16)\left( \begin{array} { r r } 4 & 5 \\- 1 & 6\end{array} \right)(4−1​56​) , B = (1−120)\left( \begin{array} { r r } 1 & - 1 \\2 & 0\end{array} \right)(12​−10​) Carry out the indicated matrix operation. ABA BAB

Fundamentals

Equations and Inequalities

Functions

Polynomial and Rational Functions Applications to Optimization

Exponential and Logarithmic Functions

An Introduction to Trigonometry Via Right Triangles

The Trigonometric Functions

Graphs of the Trigonometric Functions

Analytical Trigonometry

Additional Topics in Trigonometry

The Conic Sections

Roots of Polynomial Equations

Additional Topics in Algebra

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Solve the system using a graphing utility. $\left\{ \begin{array} { l } 0.05 x - 0.06 y = 1.41 \\0.45 x + 0.60 y = - 0.02\end{array} \right.$

Graph the inequality. $5 x - 7 y > 35$

Find all solutions of the system. $\left\{ \begin{array} { r } x + y + z = 12 \\2 x - y - z = - 5 \\6 x + 2 y + z = 30\end{array} \right.$

Find all solutions of the system. $\left\{ \begin{array} { l } x + y + z + w = 4 \\x - 2 y - z - w = 6 \\2 x - y + z - w = 5 \\x - y + 2 z - 2 w = - 5\end{array} \right.$

Use matrices to solve the system. $\left\{ \begin{aligned}5 x + y + 10 z & = 9 \\4 x + 2 y - 10 z & = 84 \\3 x - 4 y & = 11\end{aligned} \right.$

Use Cramer's rule to solve the system. $\left\{ \begin{aligned}6 x + 4 y - 2 z = & 10 \\2 x - 3 y + 4 z = & 4 \\15 x - 18 z = & - 21\end{aligned} \right.$

Find all solutions of the system. $\left\{ \begin{aligned}- x + y + z + w & = 12 \\2 y - z - w & = 7 \\2 z + 5 w & = 18 \\11 w & = 44\end{aligned} \right.$

Use the substitution method to find all solutions of the system. $\left\{ \begin{array} { l } 3 x - 2 y = - 19 \\x + 4 y = - 4\end{array} \right.$

Evaluate the determinant. $\left| \begin{array} { c c } - 4 & - 9 \\- 7 & 3\end{array} \right|$

Find all solutions of the system. $\left\{ \begin{array} { l } 2 x - 3 y + 2 z = 3 \\4 x + 2 y + 3 z = 13 \\5 x + 4 y + 2 z = 16\end{array} \right.$

Is $( 5,3 )$ a solution of the following system? $\left\{ \begin{array} { l } 5 x - 3 y = 16 \\2 x + 3 y = 19\end{array} \right.$

Use a graphing utility to compute the matrix product. $\left( \begin{array} { r r } - 38 & 18 \\23 & 8\end{array} \right)$ $\left( \begin{array} { r r } 89 & - 19 \\17 & 44\end{array} \right)$

Find the inverse, if it exists. $A = \left( \begin{array} { c c } \frac { 2 } { 9 } & - \frac { 1 } { 13 } \\- 26 & 9\end{array} \right)$

The matrices A and B are defined as follows: A = $\left( \begin{array} { r r } 4 & 5 \\- 1 & 6\end{array} \right)$ , B = $\left( \begin{array} { r r } 1 & - 1 \\2 & 0\end{array} \right)$ Carry out the indicated matrix operation. A + B

Evaluate A by expanding it along the second row. $A = \left| \begin{array} { c c c } 4 & 8 & 12 \\16 & 20 & 24 \\28 & 32 & 36\end{array} \right|$

The matrices A and B are defined as follows: A = $\left( \begin{array} { r r } 4 & 5 \\- 1 & 6\end{array} \right)$ , B = $\left( \begin{array} { r r } 1 & - 1 \\2 & 0\end{array} \right)$ Carry out the indicated matrix operation. $A B$