Question 1

Graph the equations below and determine the solution if it exists. $\left\{ \begin{array} { l } 
- 5 x - 5 y = - 10 \
10 x + 10 y = 20
\end{array} \right.$

Accepted Answer

A)  $\text { The system is consistent and has an finite number of solutions. }$   
B)  $\text { The system is consistent and has an infinite number of solutions. }$   
C)  $\text { The system is inconsistent. }$ 
  
D)  $\text { The system is consistent and has one solution whose value for } x \text { is }-3 \text { and value for } y \text { is } 2 \text {. }$
  
E)  $\text { The system is consistent and has one solution whose value for } x \text { is } 3 \text { and value for } y \text { is }-2$ 
  
A)  $\text { The system is consistent and has an finite number of solutions. }$   
B)  $\text { The system is consistent and has an infinite number of solutions. }$   
C)  $\text { The system is inconsistent. }$ 
  
D)  $\text { The system is consistent and has one solution whose value for } x \text { is }-3 \text { and value for } y \text { is } 2 \text {. }$
  
E)  $\text { The system is consistent and has one solution whose value for } x \text { is } 3 \text { and value for } y \text { is }-2$

Question 2

Write the system of linear equations represented by the augmented matrix below. Use variables x , y , z , v , and w, if necessary. 
$\left[ \begin{array} { c c c : c } 
- 9 & - 5 & - 7 & 9 \
2 & - 6 & - 6 & - 8 \
5 & - 2 & - 9 & 0
\end{array} \right]$

Accepted Answer

A)  $\left\{ \begin{array} { c } 
- 9 x - 7 z = 2 \
2 x - 6 z = - 14 \
5 x - 9 z = - 9
\end{array} \right.$ 
B)  $\left\{ \begin{array} { c } 
- 9 x - 5 y - 7 z = 9 \
2 x - 6 y - 6 z = - 8 \
5 x - 2 y - 9 z = 0
\end{array} \right.$ 
C)  $\left\{ \begin{array} { r } 
- 9 x - 5 y - 7 z = 0 \
2 x - 6 y - 6 z = 0 \
5 x - 2 y - 9 z = 0
\end{array} \right.$ 
D)  $\left\{ \begin{array} { c } 
- 9 x - 5 y = 2 \
2 x - 6 y = - 14 \
5 x - 2 y = - 9
\end{array} \right.$ 
E)  $\left\{ \begin{array} { r } 
- 9 x - 5 y - 7 z + 9 v = 0 \
2 x - 6 y - 6 z - 8 v = 0 \
5 x - 2 y - 9 z + 0 v = 0
\end{array} \right.$ 
A)  $\left\{ \begin{array} { c } 
- 9 x - 7 z = 2 \
2 x - 6 z = - 14 \
5 x - 9 z = - 9
\end{array} \right.$ 
B)  $\left\{ \begin{array} { c } 
- 9 x - 5 y - 7 z = 9 \
2 x - 6 y - 6 z = - 8 \
5 x - 2 y - 9 z = 0
\end{array} \right.$ 
C)  $\left\{ \begin{array} { r } 
- 9 x - 5 y - 7 z = 0 \
2 x - 6 y - 6 z = 0 \
5 x - 2 y - 9 z = 0
\end{array} \right.$ 
D)  $\left\{ \begin{array} { c } 
- 9 x - 5 y = 2 \
2 x - 6 y = - 14 \
5 x - 2 y = - 9
\end{array} \right.$ 
E)  $\left\{ \begin{array} { r } 
- 9 x - 5 y - 7 z + 9 v = 0 \
2 x - 6 y - 6 z - 8 v = 0 \
5 x - 2 y - 9 z + 0 v = 0
\end{array} \right.$

Question 3

Use a determinant to find the equation of the line through the points (-4,1) and (-5,-7) .

Accepted Answer

A)  $8 x + y + 12 = 0$ 
B)  $- 8 x + y + 12 = 0$ 
C)  $x - 8 y - 33 = 0$ 
D)  $x + 8 y - 33 = 0$ 
E)  $- 8 x + y - 33 = 0$ 
A)  $8 x + y + 12 = 0$ 
B)  $- 8 x + y + 12 = 0$ 
C)  $x - 8 y - 33 = 0$ 
D)  $x + 8 y - 33 = 0$ 
E)  $- 8 x + y - 33 = 0$

Question 4

Find the determinant of the matrix below. $\left[ \begin{array} { c c } 
5 & - 5 \
1 & 1
\end{array} \right]$

Accepted Answer

A)  25 
B)  10 
C)  -20 
D)  -10 
E)  -25 
A)  25 
B)  10 
C)  -20 
D)  -10 
E)  -25

Question 5

Find two positive integers that satisfy the requirements that the sum of the larger number and $\text { four }$ times the smaller number is $73$ and their difference is $3$ .

Accepted Answer

A)  $34$ and $31$ 
B)  $39$ and $36$ 
C)  $37$ and $34$ 
D)  $38$ and $35$ 
E)  $17$ and $14$ 
A)  $34$ and $31$ 
B)  $39$ and $36$ 
C)  $37$ and $34$ 
D)  $38$ and $35$ 
E)  $17$ and $14$

Question 6

Determine which ordered triple below is a solution of the system of linear equations. $\left\{ \begin{array} { r } 
3 x - 3 y - 3 z = 3 \
x - 3 y - 3 z = 7 \
2 x - 3 y - 3 z = 5
\end{array} \right.$ 
$( - 4,1 , - 2 ) , ( 1 , - 4 , - 2 ) , ( - 4 , - 2,1 ) , ( - 2,1 , - 4 )$ or $( 1 , - 2 , - 4 )$

Accepted Answer

A)  $( 1 , - 2 , - 4 )$ 
B)  $( 1 , - 4 , - 2 )$ 
C)  $( - 2,1 , - 4 )$ 
D)  $( - 4 , - 2,1 )$ 
E)  $( - 4,1 , - 2 )$ 
A)  $( 1 , - 2 , - 4 )$ 
B)  $( 1 , - 4 , - 2 )$ 
C)  $( - 2,1 , - 4 )$ 
D)  $( - 4 , - 2,1 )$ 
E)  $( - 4,1 , - 2 )$

Question 7

Graph the system of linear inequalities below. $$\left\{ \begin{array} { l } 
x - 3 y > - 6 \
3 x + y > 2
\end{array} \right.$$

Accepted Answer

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

Question 8

Determine if the ordered pair $( 18,0 )$ is a solution of the system of linear inequalities $\left\{ \begin{array} { l } 
3 x - y > 4 \
x + 6 y \leq 9
\end{array} \right.$ .

Accepted Answer

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

Question 9

Find a system of linear equations below that has the point $( - 1,0,4 )$ as a solution. $\left\{ \begin{array} { l } 
4 x - 2 y + 4 z = 12 \
2 x - 6 y + 8 z = 30 \
7 x - 3 y + 6 z = 17
\end{array} \right.$ , $\left\{ \begin{array} { l } 
4 x - 2 y + 4 z = 30 \
2 x - 6 y + 8 z = 17 \
7 x - 3 y + 6 z = 12
\end{array} \right.$ , $\left\{ \begin{array} { l } 
4 x - 2 y + 4 z = 17 \
2 x - 6 y + 8 z = 12 \
7 x - 3 y + 6 z = 30
\end{array} \right.$ , $\left\{ \begin{array} { l } 
4 x - 2 y + 4 z = 12 \
2 x - 6 y + 8 z = 17 \
7 x - 3 y + 6 z = 30
\end{array} \right.$ or $\left\{ \begin{array} { l } 
4 x - 2 y + 4 z = 30 \
2 x - 6 y + 8 z = 12 \
7 x - 3 y + 6 z = 17
\end{array} \right.$

Accepted Answer

A)  $\left\{ \begin{array} { c } 
4 x - 2 y + 4 = 17 \
2 x - 6 y + 8 z = 12 \
7 x - 3 y + 6 z = 30
\end{array} \right.$ 
B)  $\left\{ \begin{array} { l } 
4 x - 2 y + 4 z = 12 \
2 x - 6 y + 8 z = 30 \
7 x - 3 y + 6 z = 17
\end{array} \right.$ 
C)  $\left\{ \begin{array} { l } 
4 x - 2 y + 4 z = 30 \
2 x - 6 y + 8 z = 12 \
7 x - 3 y + 6 z = 17
\end{array} \right.$ 
D)  $\left\{ \begin{array} { c } 
4 x - 2 y + 4 = 12 \
2 x - 6 y + 8 z = 17 \
7 x - 3 y + 6 z = 30
\end{array} \right.$ 
E)  $\left\{ \begin{array} { c } 
4 x - 2 y + 4 = 30 \
2 x - 6 y + 8 z = 17 \
7 x - 3 y + 6 z = 12
\end{array} \right.$ 
A)  $\left\{ \begin{array} { c } 
4 x - 2 y + 4 = 17 \
2 x - 6 y + 8 z = 12 \
7 x - 3 y + 6 z = 30
\end{array} \right.$ 
B)  $\left\{ \begin{array} { l } 
4 x - 2 y + 4 z = 12 \
2 x - 6 y + 8 z = 30 \
7 x - 3 y + 6 z = 17
\end{array} \right.$ 
C)  $\left\{ \begin{array} { l } 
4 x - 2 y + 4 z = 30 \
2 x - 6 y + 8 z = 12 \
7 x - 3 y + 6 z = 17
\end{array} \right.$ 
D)  $\left\{ \begin{array} { c } 
4 x - 2 y + 4 = 12 \
2 x - 6 y + 8 z = 17 \
7 x - 3 y + 6 z = 30
\end{array} \right.$ 
E)  $\left\{ \begin{array} { c } 
4 x - 2 y + 4 = 30 \
2 x - 6 y + 8 z = 17 \
7 x - 3 y + 6 z = 12
\end{array} \right.$

Question 10

An airplane flying into a headwind travels 2016 miles in 4 hours and 12 minutes. On the return flight, the same distance is traveled in 4 hours. Find the speed of the plane in still air, assuming that both the speed of the plane and the speed of the air remains constant throughout the round trip. Round to the nearest miles.

Accepted Answer

A) 468 miles per hour 
B) 492 miles per hour 
C) 516 miles per hour 
D) 480 miles per hour 
E) 504 miles per hour 
A) 468 miles per hour 
B) 492 miles per hour 
C) 516 miles per hour 
D) 480 miles per hour 
E) 504 miles per hour

Question 11

Use Cramer s Rule to solve the system of linear equations. $\left\{ \begin{array} { l } 
8 x + 6 y - 8 z = - 141 \
x + 5 y - 9 z = - 464 \
- 2 x + 3 y - 4 z = - 354
\end{array} \right.$

Accepted Answer

A)  $\left( \frac { 83 } { 4 } , - \frac { 189 } { 2 } , \frac { 135 } { 4 } \right)$ 
B)  $\left( \frac { 135 } { 4 } , \frac { 189 } { 4 } , - \frac { 83 } { 2 } \right)$ 
C)  $\left( \frac { 189 } { 4 } , \frac { 135 } { 4 } , - \frac { 83 } { 2 } \right)$ 
D)  $\left( \frac { 189 } { 4 } , - \frac { 83 } { 2 } , \frac { 135 } { 4 } \right)$ 
E)  $\left( - \frac { 83 } { 2 } , \frac { 135 } { 4 } , \frac { 189 } { 4 } \right)$ 
A)  $\left( \frac { 83 } { 4 } , - \frac { 189 } { 2 } , \frac { 135 } { 4 } \right)$ 
B)  $\left( \frac { 135 } { 4 } , \frac { 189 } { 4 } , - \frac { 83 } { 2 } \right)$ 
C)  $\left( \frac { 189 } { 4 } , \frac { 135 } { 4 } , - \frac { 83 } { 2 } \right)$ 
D)  $\left( \frac { 189 } { 4 } , - \frac { 83 } { 2 } , \frac { 135 } { 4 } \right)$ 
E)  $\left( - \frac { 83 } { 2 } , \frac { 135 } { 4 } , \frac { 189 } { 4 } \right)$

Question 12

Solve the system of equations below by the method of substitution. $\left\{ \begin{array} { l } 
11 x - y = 20 \
- 8 x - 15 y = - 46
\end{array} \right.$

Accepted Answer

A)  (0,-6) 
B)  (8,-2) 
C)  (2,0) 
D)  (9,-1) 
E)  (2,2) 
A)  (0,-6) 
B)  (8,-2) 
C)  (2,0) 
D)  (9,-1) 
E)  (2,2)

Question 13

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

Accepted Answer

A)  $\left( - \frac { 11 } { 12 } , \frac { 1 } { 2 } \right)$ 
B)  $\left( \frac { 11 } { 12 } , \frac { 3 } { 2 } \right)$ 
C)  $\left( - \frac { 1 } { 12 } , \frac { 1 } { 3 } \right)$ 
D)  $\left( - \frac { 1 } { 4 } , \frac { 7 } { 4 } \right)$ 
E)  $\left( \frac { 5 } { 4 } , - \frac { 3 } { 2 } \right)$ 
A)  $\left( - \frac { 11 } { 12 } , \frac { 1 } { 2 } \right)$ 
B)  $\left( \frac { 11 } { 12 } , \frac { 3 } { 2 } \right)$ 
C)  $\left( - \frac { 1 } { 12 } , \frac { 1 } { 3 } \right)$ 
D)  $\left( - \frac { 1 } { 4 } , \frac { 7 } { 4 } \right)$ 
E)  $\left( \frac { 5 } { 4 } , - \frac { 3 } { 2 } \right)$

Question 14

Solve the system of linear equations by the method of elimination and identify the grey line in the graph with its linear equation. $\left\{ \begin{array} { c } 
6 x - 6 y = - 48 \
x + 4 y = 12
\end{array} \right.$

Accepted Answer

A) The solution is (-4,4) and the equation of the grey line is $6 x - 6 y = - 48$ . 
B) The solution is (-4,4) and the equation of the grey line is $x + 4 y = - 20$ . 
C) The solution is (-4,4) and the equation of the grey line is $6 x - 6 y = - 48$ . 
D) The solution is $( 4 , - 4 )$ and the equation of the grey line is $6 x - 6 y = - 48$ . 
E) The solution is $( 4 , - 4 )$ and the equation of the grey line is $6 x - 6 y = - 48$ . 
A) The solution is (-4,4) and the equation of the grey line is $6 x - 6 y = - 48$ . 
B) The solution is (-4,4) and the equation of the grey line is $x + 4 y = - 20$ . 
C) The solution is (-4,4) and the equation of the grey line is $6 x - 6 y = - 48$ . 
D) The solution is $( 4 , - 4 )$ and the equation of the grey line is $6 x - 6 y = - 48$ . 
E) The solution is $( 4 , - 4 )$ and the equation of the grey line is $6 x - 6 y = - 48$ .

Question 15

Determine whether the points (1,1) , (-3,1) , and (-7,1) are collinear.

Accepted Answer

A) The points are not collinear. 
B) The points are collinear. 
A) The points are not collinear. 
B) The points are collinear.

Question 16

Convert the matrix to row-echelon form. $\left[ \begin{array} { c c c c } 
1 & - 3 & 2 & 3 \
- 2 & 9 & - 6 & - 6 \
- 1 & 6 & - 5 & 0
\end{array} \right]$

Accepted Answer

A)  $\left[ \begin{array} { l l l l } 
1 & 1 & 2 & - 2 \
0 & 1 & 0 & - 3 \
0 & 0 & 1 & - 3
\end{array} \right]$ 
B)  $\left[ \begin{array} { c c c c } 
1 & - 3 & 2 & 3 \
0 & 1 & 0 & - 2 \
0 & 0 & 1 & - 3
\end{array} \right]$ 
C)  $\left[ \begin{array} { c c c c } 
1 & 3 & - 3 & - 2 \
0 & 1 & 0 & - 1 \
0 & 0 & 1 & - 2
\end{array} \right]$ 
D)  $\left[ \begin{array} { c c c c } 
1 & 0 & 2 & 0 \
0 & 1 & - 2 & 0 \
0 & 0 & 1 & - 3
\end{array} \right]$ 
E)  $\left[ \begin{array} { c c c c } 
1 & 2 & 2 & 1 \
0 & 1 & 0 & 6 \
0 & 0 & 1 & - 3
\end{array} \right]$ 
A)  $\left[ \begin{array} { l l l l } 
1 & 1 & 2 & - 2 \
0 & 1 & 0 & - 3 \
0 & 0 & 1 & - 3
\end{array} \right]$ 
B)  $\left[ \begin{array} { c c c c } 
1 & - 3 & 2 & 3 \
0 & 1 & 0 & - 2 \
0 & 0 & 1 & - 3
\end{array} \right]$ 
C)  $\left[ \begin{array} { c c c c } 
1 & 3 & - 3 & - 2 \
0 & 1 & 0 & - 1 \
0 & 0 & 1 & - 2
\end{array} \right]$ 
D)  $\left[ \begin{array} { c c c c } 
1 & 0 & 2 & 0 \
0 & 1 & - 2 & 0 \
0 & 0 & 1 & - 3
\end{array} \right]$ 
E)  $\left[ \begin{array} { c c c c } 
1 & 2 & 2 & 1 \
0 & 1 & 0 & 6 \
0 & 0 & 1 & - 3
\end{array} \right]$

Question 17

Use the graphs of the equations to determine whether the system has any solutions. Find any solutions that exist. 
$\left\{ \begin{array} { l } 
- 5 x - 5 y = - 10 \
10 x + 10 y = 20
\end{array} \right.$

Accepted Answer

A)  $\text { The system is consistent and has one solution whose value for } x \text { is }-3 \text { and value for } y \text { is } 2$ 
B)  $\text { The system is consistent and has an finite number of solutions. }$ 
C)  $\text { The system is consistent and has an infinite number of solutions. }$ 
D)  $\text { The system is consistent and has one solution whose value for } x \text { is } 3 \text { and value for } y \text { is }-2 \text {. }$ 
E)  $\text { The system is inconsistent. }$ 
A)  $\text { The system is consistent and has one solution whose value for } x \text { is }-3 \text { and value for } y \text { is } 2$ 
B)  $\text { The system is consistent and has an finite number of solutions. }$ 
C)  $\text { The system is consistent and has an infinite number of solutions. }$ 
D)  $\text { The system is consistent and has one solution whose value for } x \text { is } 3 \text { and value for } y \text { is }-2 \text {. }$ 
E)  $\text { The system is inconsistent. }$

Question 18

Decide whether the system $\left\{ \begin{array} { c } 
3 x - 6 y = 6 \
- 12 x + 24 y = - 24
\end{array} \right.$ is consistent or inconsistent.

Accepted Answer

A) inconsistent 
B) consistent 
A) inconsistent 
B) consistent

Question 19

To open a small business, you need an initial investment of $150,000. Each week your costs will be about $8,850. Your projected weekly revenue is $9,700. How many weeks will it take to break even? Round to the nearest number of weeks.

Accepted Answer

A) 17 weeks 
B) 182 weeks 
C) 177 weeks 
D) 16 weeks 
E) 179 weeks 
A) 17 weeks 
B) 182 weeks 
C) 177 weeks 
D) 16 weeks 
E) 179 weeks

Question 20

Use Cramer s Rule to solve the system of linear equations below. $\left\{ \begin{array} { l } 
x - 4 y - 2 z = 13 \
3 x + 2 y - z = - 12 \
4 x - 3 y + 2 z = 10
\end{array} \right.$

Accepted Answer

A)  $( - 6,0,3 )$ 
B)  $( - 1 , - 4,1 )$ 
C)  $( - 5,4,3 )$ 
D)  $( 5,1,0 )$ 
E)  $( - 3,4 , - 3 )$ 
A)  $( - 6,0,3 )$ 
B)  $( - 1 , - 4,1 )$ 
C)  $( - 5,4,3 )$ 
D)  $( 5,1,0 )$ 
E)  $( - 3,4 , - 3 )$

Graph the equations below and determine the solution if it exists. $\left\{ \begin{array} { l } - 5 x - 5 y = - 10 \\10 x + 10 y = 20\end{array} \right.$

Write the system of linear equations represented by the augmented matrix below. Use variables x , y , z , v , and w, if necessary. $\left[ \begin{array} { c c c : c } - 9 & - 5 & - 7 & 9 \\2 & - 6 & - 6 & - 8 \\5 & - 2 & - 9 & 0\end{array} \right]$

Use a determinant to find the equation of the line through the points (-4,1) and (-5,-7) .

Find the determinant of the matrix below. $\left[ \begin{array} { c c } 5 & - 5 \\1 & 1\end{array} \right]$

Find two positive integers that satisfy the requirements that the sum of the larger number and $\text { four }$ times the smaller number is $73$ and their difference is $3$ .

Determine which ordered triple below is a solution of the system of linear equations. $\left\{ \begin{array} { r } 3 x - 3 y - 3 z = 3 \\x - 3 y - 3 z = 7 \\2 x - 3 y - 3 z = 5\end{array} \right.$ $( - 4,1 , - 2 ) , ( 1 , - 4 , - 2 ) , ( - 4 , - 2,1 ) , ( - 2,1 , - 4 )$ or $( 1 , - 2 , - 4 )$

Graph the system of linear inequalities below. $\left\{ \begin{array} { l } x - 3 y > - 6 \\3 x + y > 2\end{array} \right.$

Determine if the ordered pair $( 18,0 )$ is a solution of the system of linear inequalities $\left\{ \begin{array} { l } 3 x - y > 4 \\x + 6 y \leq 9\end{array} \right.$ .

Use Cramer s Rule to solve the system of linear equations. $\left\{ \begin{array} { l } 8 x + 6 y - 8 z = - 141 \\x + 5 y - 9 z = - 464 \\- 2 x + 3 y - 4 z = - 354\end{array} \right.$

Solve the system of equations below by the method of substitution. $\left\{ \begin{array} { l } 11 x - y = 20 \\- 8 x - 15 y = - 46\end{array} \right.$

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

Determine whether the points (1,1) , (-3,1) , and (-7,1) are collinear.

Convert the matrix to row-echelon form. $\left[ \begin{array} { c c c c } 1 & - 3 & 2 & 3 \\- 2 & 9 & - 6 & - 6 \\- 1 & 6 & - 5 & 0\end{array} \right]$

Decide whether the system $\left\{ \begin{array} { c } 3 x - 6 y = 6 \\- 12 x + 24 y = - 24\end{array} \right.$ is consistent or inconsistent.

To open a small business, you need an initial investment of $150,000. Each week your costs will be about $8,850. Your projected weekly revenue is $9,700. How many weeks will it take to break even? Round to the nearest number of weeks.

Use Cramer s Rule to solve the system of linear equations below. $\left\{ \begin{array} { l } x - 4 y - 2 z = 13 \\3 x + 2 y - z = - 12 \\4 x - 3 y + 2 z = 10\end{array} \right.$

Fundamentals of Algebra

Linear Equations and Inequalities

Graphs and Functions

Polynomials and Factoring

Rational Expressions, Equations, and Functions

Radicals and Complex Numbers

Quadratic Equations, Functions, and Inequalities

Exponential and Logarithmic Functions

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Sequences, Series, and the Binomial Theorem

Filters

Exam 4: Systems of Equations and Inequalities

Graph the equations below and determine the solution if it exists. {−5x−5y=−1010x+10y=20\left\{ \begin{array} { l } - 5 x - 5 y = - 10 \\10 x + 10 y = 20\end{array} \right.{−5x−5y=−1010x+10y=20​

Use a determinant to find the equation of the line through the points (-4,1) and (-5,-7) .

Find the determinant of the matrix below. [5−511]\left[ \begin{array} { c c } 5 & - 5 \\1 & 1\end{array} \right][51​−51​]

Find two positive integers that satisfy the requirements that the sum of the larger number and four \text { four } four times the smaller number is 737373 and their difference is 333 .

Graph the system of linear inequalities below. {x−3y>−63x+y>2\left\{ \begin{array} { l } x - 3 y > - 6 \\3 x + y > 2\end{array} \right.{x−3y>−63x+y>2​

Determine if the ordered pair (18,0)( 18,0 )(18,0) is a solution of the system of linear inequalities {3x−y>4x+6y≤9\left\{ \begin{array} { l } 3 x - y > 4 \\x + 6 y \leq 9\end{array} \right.{3x−y>4x+6y≤9​ .

Solve the system of equations below by the method of substitution. {11x−y=20−8x−15y=−46\left\{ \begin{array} { l } 11 x - y = 20 \\- 8 x - 15 y = - 46\end{array} \right.{11x−y=20−8x−15y=−46​

Solve the system of linear equations by the method of elimination and identify the grey line in the graph with its linear equation. {6x−6y=−48x+4y=12\left\{ \begin{array} { c } 6 x - 6 y = - 48 \\x + 4 y = 12\end{array} \right.{6x−6y=−48x+4y=12​

Determine whether the points (1,1) , (-3,1) , and (-7,1) are collinear.

Convert the matrix to row-echelon form. [1−323−29−6−6−16−50]\left[ \begin{array} { c c c c } 1 & - 3 & 2 & 3 \\- 2 & 9 & - 6 & - 6 \\- 1 & 6 & - 5 & 0\end{array} \right]​1−2−1​−396​2−6−5​3−60​​

Use the graphs of the equations to determine whether the system has any solutions. Find any solutions that exist. {−5x−5y=−1010x+10y=20\left\{ \begin{array} { l } - 5 x - 5 y = - 10 \\10 x + 10 y = 20\end{array} \right.{−5x−5y=−1010x+10y=20​

Decide whether the system {3x−6y=6−12x+24y=−24\left\{ \begin{array} { c } 3 x - 6 y = 6 \\- 12 x + 24 y = - 24\end{array} \right.{3x−6y=6−12x+24y=−24​ is consistent or inconsistent.

To open a small business, you need an initial investment of $150,000. Each week your costs will be about $8,850. Your projected weekly revenue is $9,700. How many weeks will it take to break even? Round to the nearest number of weeks.

Use Cramer s Rule to solve the system of linear equations below. {x−4y−2z=133x+2y−z=−124x−3y+2z=10\left\{ \begin{array} { l } x - 4 y - 2 z = 13 \\3 x + 2 y - z = - 12 \\4 x - 3 y + 2 z = 10\end{array} \right.⎩⎨⎧​x−4y−2z=133x+2y−z=−124x−3y+2z=10​

Fundamentals of Algebra

Linear Equations and Inequalities

Graphs and Functions

Polynomials and Factoring

Rational Expressions, Equations, and Functions

Radicals and Complex Numbers

Quadratic Equations, Functions, and Inequalities

Exponential and Logarithmic Functions

Conics

Sequences, Series, and the Binomial Theorem

Filters

Graph the equations below and determine the solution if it exists. $\left\{ \begin{array} { l } - 5 x - 5 y = - 10 \\10 x + 10 y = 20\end{array} \right.$

Find the determinant of the matrix below. $\left[ \begin{array} { c c } 5 & - 5 \\1 & 1\end{array} \right]$

Find two positive integers that satisfy the requirements that the sum of the larger number and $\text { four }$ times the smaller number is $73$ and their difference is $3$ .

Graph the system of linear inequalities below. $\left\{ \begin{array} { l } x - 3 y > - 6 \\3 x + y > 2\end{array} \right.$

Determine if the ordered pair $( 18,0 )$ is a solution of the system of linear inequalities $\left\{ \begin{array} { l } 3 x - y > 4 \\x + 6 y \leq 9\end{array} \right.$ .

Solve the system of equations below by the method of substitution. $\left\{ \begin{array} { l } 11 x - y = 20 \\- 8 x - 15 y = - 46\end{array} \right.$

Convert the matrix to row-echelon form. $\left[ \begin{array} { c c c c } 1 & - 3 & 2 & 3 \\- 2 & 9 & - 6 & - 6 \\- 1 & 6 & - 5 & 0\end{array} \right]$

Decide whether the system $\left\{ \begin{array} { c } 3 x - 6 y = 6 \\- 12 x + 24 y = - 24\end{array} \right.$ is consistent or inconsistent.

Use Cramer s Rule to solve the system of linear equations below. $\left\{ \begin{array} { l } x - 4 y - 2 z = 13 \\3 x + 2 y - z = - 12 \\4 x - 3 y + 2 z = 10\end{array} \right.$