Question 1

Solve system by the method of substitution and graph your solution.
$$\left\{ \begin{array} { l } 
y = x ^ { 3 } + 3 x ^ { 2 } + 2 x \
y = - x
\end{array} \right.$$

Accepted Answer

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

Question 2

Given:
$A = \left[ \begin{array} { r r r } 8 & - 7 & 0 \ - 5 & - 2 & 3 \end{array} \right] , B = \left[ \begin{array} { r r r } 3 & 0 & 7 \ 4 & 9 & - 2 \end{array} \right] , c = 8$ and $d = - 3$, determine $c A + d B$.

Accepted Answer

A)  $\left[ \begin{array} { r r r } 55 & - 7 & 7 \ - 52 & 7 & 1 \end{array} \right]$ 
B)  $\left[ \begin{array} { r r r } 73 & - 56 & 21 \ - 28 & 11 & 18 \end{array} \right]$ 
C)  $\left[ \begin{array} { r r r } 55 & - 56 & - 21 \ - 52 & - 43 & 30 \end{array} \right]$ 
D)  $\left[ \begin{array} { r r r } 55 & - 56 & - 21 \ - 1 & 7 & 1 \end{array} \right]$ 
E)  not possible 
A)  $\left[ \begin{array} { r r r } 55 & - 7 & 7 \ - 52 & 7 & 1 \end{array} \right]$ 
B)  $\left[ \begin{array} { r r r } 73 & - 56 & 21 \ - 28 & 11 & 18 \end{array} \right]$ 
C)  $\left[ \begin{array} { r r r } 55 & - 56 & - 21 \ - 52 & - 43 & 30 \end{array} \right]$ 
D)  $\left[ \begin{array} { r r r } 55 & - 56 & - 21 \ - 1 & 7 & 1 \end{array} \right]$ 
E)  not possible

Question 3

Find a system of linear equations that has the following solution.
$$\left( - \frac { 4 } { 7 } , 10 \right)$$

Accepted Answer

A) $\left\{ \begin{array} { l } 28 x + 15 y = \frac { 1900 } { 7 } \ 56 x + 10 y = \frac { 3880 } { 7 } \end{array} \right.$ 
B)  $\left\{ \begin{array} { l } 28 y + 15 x = 134 \ 56 y + 10 x = 68 \end{array} \right.$ 
C)  $\left\{ \begin{array} { l } 56 x + 10 y = - 166 \ 28 x + 15 y = - 132 \end{array} \right.$ 
D) $\left\{ \begin{array} { l } 28 y + 15 x = \frac { 1900 } { 7 } \ 56 y + 10 x = \frac { 3880 } { 7 } \end{array} \right.$ 
E)  $\left\{ \begin{array} { l } 28 x + 15 y = 134 \ 56 x + 10 y = 68 \end{array} \right.$ 
A) $\left\{ \begin{array} { l } 28 x + 15 y = \frac { 1900 } { 7 } \ 56 x + 10 y = \frac { 3880 } { 7 } \end{array} \right.$ 
B)  $\left\{ \begin{array} { l } 28 y + 15 x = 134 \ 56 y + 10 x = 68 \end{array} \right.$ 
C)  $\left\{ \begin{array} { l } 56 x + 10 y = - 166 \ 28 x + 15 y = - 132 \end{array} \right.$ 
D) $\left\{ \begin{array} { l } 28 y + 15 x = \frac { 1900 } { 7 } \ 56 y + 10 x = \frac { 3880 } { 7 } \end{array} \right.$ 
E)  $\left\{ \begin{array} { l } 28 x + 15 y = 134 \ 56 x + 10 y = 68 \end{array} \right.$

Question 4

Evaluate the expression.
$$\frac { 1 } { 4 } \left[ \begin{array} { l l l } 
- 9 & 1 & - 1
\end{array} \right] + \left[ \begin{array} { l l l } 
- 4 & - 6 & 8
\end{array} \right]$$

Accepted Answer

A)  $\left[ \begin{array} { l l l } - 13 & - 5 & 7 \end{array} \right]$ 
B)  $\left[ \begin{array} { l l l } \frac { 7 } { 4 } & \frac { 25 } { 4 } & - \frac { 33 } { 4 } \end{array} \right]$ 
C)  $\left[ \begin{array} { l l l } - \frac { 13 } { 4 } & - \frac { 5 } { 4 } & \frac { 7 } { 4 } \end{array} \right]$ 
D)  $\left[ \begin{array} { l l l } - \frac { 25 } { 4 } & - \frac { 23 } { 4 } & \frac { 31 } { 4 } \end{array} \right]$ 
E)  not possible 
A)  $\left[ \begin{array} { l l l } - 13 & - 5 & 7 \end{array} \right]$ 
B)  $\left[ \begin{array} { l l l } \frac { 7 } { 4 } & \frac { 25 } { 4 } & - \frac { 33 } { 4 } \end{array} \right]$ 
C)  $\left[ \begin{array} { l l l } - \frac { 13 } { 4 } & - \frac { 5 } { 4 } & \frac { 7 } { 4 } \end{array} \right]$ 
D)  $\left[ \begin{array} { l l l } - \frac { 25 } { 4 } & - \frac { 23 } { 4 } & \frac { 31 } { 4 } \end{array} \right]$ 
E)  not possible

Question 5

Use a system of equations to find the specified equation that passes through the points.
Solve the system using matrices.
Parabola: $y = a x ^ { 2 } + b x + c$

Accepted Answer

A)  $y = - x ^ { 2 } - 12$ 
B)  $y = - x ^ { 2 } - x - 12$ 
C)  $y = x ^ { 2 } + x - 12$ 
D)  $y = x ^ { 2 } + 9 x - 36$ 
E)  $y = x ^ { 2 } - 12$ 
A)  $y = - x ^ { 2 } - 12$ 
B)  $y = - x ^ { 2 } - x - 12$ 
C)  $y = x ^ { 2 } + x - 12$ 
D)  $y = x ^ { 2 } + 9 x - 36$ 
E)  $y = x ^ { 2 } - 12$

Question 6

Solve the system by the method of elimination. Round numbers to three decimal places.
$$\left\{ \begin{array} { c } 
5.2 x + 8.1 y = 6.9 \
- 2.6 x + 1.1 y = - 0.7
\end{array} \right.$$

Accepted Answer

A)  $( 2.020,1.873 )$ 
B)  $( 0.495,0.534 )$ 
C)  $( - 0.864,1.407 )$ 
D)  $( 0.192,0.728 )$ 
E)  no solution 
A)  $( 2.020,1.873 )$ 
B)  $( 0.495,0.534 )$ 
C)  $( - 0.864,1.407 )$ 
D)  $( 0.192,0.728 )$ 
E)  no solution

Question 7

Solve the system of equations below using Gaussian elimination.
$$\begin{aligned}
5 x + 4 y + 3 z & = 54 \
x - 2 y + 2 z & = 36 \
x - y - z & = - 18
\end{aligned}$$

Accepted Answer

A)  $( 1 , - 1,20 )$ 
B)  $( 1,0,19 )$ 
C)  $( 0,1,17 )$ 
D)  $( - 1,1,16 )$ 
E)  $( 0,0,18 )$ 
A)  $( 1 , - 1,20 )$ 
B)  $( 1,0,19 )$ 
C)  $( 0,1,17 )$ 
D)  $( - 1,1,16 )$ 
E)  $( 0,0,18 )$

Question 8

Solve system of equations by the method of substitution. $$\left\{ \begin{array} { r } 
15 x ^ { 3 } - 25 y = 0 \
15 x - y = 0
\end{array} \right.$$

Accepted Answer

A)  (0,0) , (-5, -75) , (5,75) 
B)  (0,0) , (-5,75) , (5,75) 
C)  (0,0) , (5, -75) , (5,75) 
D)  (0,0) , (-5,76) , (5,76) 
E)  (0,0) , (-5, -74) , (5,74) 
A)  (0,0) , (-5, -75) , (5,75) 
B)  (0,0) , (-5,75) , (5,75) 
C)  (0,0) , (5, -75) , (5,75) 
D)  (0,0) , (-5,76) , (5,76) 
E)  (0,0) , (-5, -74) , (5,74)

Question 9

Solve for X in the equation given. $9 A + 6 B = 3 X , A = \left[ \begin{array} { c c c } 6 & - 5 & 3 \ 8 & - 3 & - 7 \end{array} \right]$ and $B = \left[ \begin{array} { c c c } 3 & 5 & - 1 \ 1 & - 2 & 5 \end{array} \right]$

Accepted Answer

A)  $\left[ \begin{array} { c c c } 72 & - 15 & 21 \ 78 & - 39 & - 33 \end{array} \right]$ 
B)  $\left[ \begin{array} { c c c } 9 & 0 & 2 \ 9 & - 5 & - 2 \end{array} \right]$ 
C)  $\left[ \begin{array} { c c c } 24 & - 5 & 7 \ 26 & - 13 & - 11 \end{array} \right]$ 
D)  $\left[ \begin{array} { c c c } 12 & - 25 & 11 \ 22 & - 5 & - 31 \end{array} \right]$ 
E)  not possible 
A)  $\left[ \begin{array} { c c c } 72 & - 15 & 21 \ 78 & - 39 & - 33 \end{array} \right]$ 
B)  $\left[ \begin{array} { c c c } 9 & 0 & 2 \ 9 & - 5 & - 2 \end{array} \right]$ 
C)  $\left[ \begin{array} { c c c } 24 & - 5 & 7 \ 26 & - 13 & - 11 \end{array} \right]$ 
D)  $\left[ \begin{array} { c c c } 12 & - 25 & 11 \ 22 & - 5 & - 31 \end{array} \right]$ 
E)  not possible

Question 10

Find $| A B |$, if
$$A = \left[ \begin{array} { r r r } 
- 3 & 4 & 5 \
- 3 & - 5 & 1 \
5 & - 5 & 1
\end{array} \right] , B = \left[ \begin{array} { r r r } 
- 1 & - 2 & 5 \
4 & 1 & - 3 \
- 1 & - 1 & 4
\end{array} \right]$$

Accepted Answer

A)  2320 
B)  2736 
C)  202 
D)  0 
E)  $- 2644$ 
A)  2320 
B)  2736 
C)  202 
D)  0 
E)  $- 2644$

Question 11

Use the matrix capabilities of a graphing utility to find the inverse of the matrix $\frac { 1 } { 6 } \left[ \begin{array} { c c c } - 4 & - 5 & 3 \ - 4 & - 8 & 3 \ 1 & 2 & 0 \end{array} \right]$ (if it exists).

Accepted Answer

A)  $\left[ \begin{array} { c c c } 2 & 2 & 6 \ 0 & - 2 & 0 \ 0 & 4 & 8 \end{array} \right]$ 
B)  $\left[ \begin{array} { c c c } - 6 & 8 & 4 \ 0 & - 2 & 0 \ 0 & 2 & - 6 \end{array} \right]$ 
C)  $\left[ \begin{array} { c c c } - 4 & 0 & 6 \ 0 & - 2 & 0 \ 0 & 2 & - 4 \end{array} \right]$ 
D)  $\left[ \begin{array} { c c c } - 4 & 4 & 6 \ 2 & - 2 & 0 \ 0 & 2 & 8 \end{array} \right]$ 
E)  does not exist 
A)  $\left[ \begin{array} { c c c } 2 & 2 & 6 \ 0 & - 2 & 0 \ 0 & 4 & 8 \end{array} \right]$ 
B)  $\left[ \begin{array} { c c c } - 6 & 8 & 4 \ 0 & - 2 & 0 \ 0 & 2 & - 6 \end{array} \right]$ 
C)  $\left[ \begin{array} { c c c } - 4 & 0 & 6 \ 0 & - 2 & 0 \ 0 & 2 & - 4 \end{array} \right]$ 
D)  $\left[ \begin{array} { c c c } - 4 & 4 & 6 \ 2 & - 2 & 0 \ 0 & 2 & 8 \end{array} \right]$ 
E)  does not exist

Question 12

Solve the system by the method of elimination.
$$\left\{ \begin{array} { c } 
\frac { 1 } { 9 } x - \frac { 1 } { 8 } y = 6 \
- 48 x + 54 y = - 2591
\end{array} \right.$$

Accepted Answer

A)  $( 9 , - 40 )$ 
B)  no solution 
C)  $\left( \frac { 2915 } { 102 } , - \frac { 2303 } { 102 } \right)$ 
D)  $\left( \frac { 5183 } { 96 } , \frac { 1 } { 108 } \right)$ 
E)  infinitely many solutions 
A)  $( 9 , - 40 )$ 
B)  no solution 
C)  $\left( \frac { 2915 } { 102 } , - \frac { 2303 } { 102 } \right)$ 
D)  $\left( \frac { 5183 } { 96 } , \frac { 1 } { 108 } \right)$ 
E)  infinitely many solutions

Question 13

Solve the system by the method of elimination.
$$\left\{ \begin{aligned}
4 x + 5 y & = - 71 \
x - y & = - 2
\end{aligned} \right.$$

Accepted Answer

A)  $( - 6 , - 4 )$ 
B)  $( - 9 , - 7 )$ 
C)  $\left( - \frac { 61 } { 3 } , \frac { 52 } { 3 } \right)$ 
D)  $\left( 8 , - \frac { 111 } { 4 } \right)$ 
E)  inconsistent 
A)  $( - 6 , - 4 )$ 
B)  $( - 9 , - 7 )$ 
C)  $\left( - \frac { 61 } { 3 } , \frac { 52 } { 3 } \right)$ 
D)  $\left( 8 , - \frac { 111 } { 4 } \right)$ 
E)  inconsistent

Question 14

Solve the system of linear equations.
$$\left\{ \begin{array} { c } 
x + 5 y + 5 z = 9 \
- 2 x + z = - 6 \
2 x + 4 y - 3 z = - 2
\end{array} \right.$$

Accepted Answer

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

Question 15

Solve the system of linear equations.
$$\left\{ \begin{aligned}
x + y + z & = - 6 \
x - 6 y - 7 z & = 76 \
8 y - 6 z & = - 18
\end{aligned} \right.$$

Accepted Answer

A)  $( 4 , - 7 , - 3 )$ 
B)  $( - 7,4 , - 3 )$ 
C)  $( 5 , - 6 , - 5 )$ 
D)  $( - 6,5 , - 5 )$ 
E)  $( 8 , - 8 , - 6 )$ 
A)  $( 4 , - 7 , - 3 )$ 
B)  $( - 7,4 , - 3 )$ 
C)  $( 5 , - 6 , - 5 )$ 
D)  $( - 6,5 , - 5 )$ 
E)  $( 8 , - 8 , - 6 )$

Question 16

Determine which ordered pair is a solution of the system.
$$\left\{ \begin{aligned}
x - 2 y ^ { 2 } & = - 7 \
- 5 x + 6 y & = 7
\end{aligned} \right.$$

Accepted Answer

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

Question 17

Determine whether the two systems of linear equations yield the same solutions. If so, find the solutions using matrices.
$\left\{ \begin{array} { r } x + 9 y - 2 z = 41 \ y - 7 z = 46 \ z = - 6 \end{array} \right.$
$\left\{ \begin{aligned} x + 4 y + 2 z & = - 3 \ y + 5 z & = - 26 \ z & = - 6 \end{aligned} \right.$

Accepted Answer

A)  $x = - 7 , y = 4 , z = - 6$ 
B)  $x = 7 , y = - 4 , z = - 6$ 
C)  $x = - 4 , y = - 6 , z = - 7$ 
D)  $x = 4 , y = - 6 , z = - 7$ 
E)  The systems yield different solutions. 
A)  $x = - 7 , y = 4 , z = - 6$ 
B)  $x = 7 , y = - 4 , z = - 6$ 
C)  $x = - 4 , y = - 6 , z = - 7$ 
D)  $x = 4 , y = - 6 , z = - 7$ 
E)  The systems yield different solutions.

Question 18

Identify the elementary row operation being performed to obtain the new rowequivalent matrix.

Accepted Answer

A)  Add 5 times $R _ { 1 }$ to $R _ { 2 }$. 
B)  Add $- 5$ times $R _ { 2 }$ to $R _ { 1 }$. 
C)  Add $- 5$ times $R _ { 1 }$ to $R _ { 2 }$. 
D)  Add 5 times $R _ { 1 }$ to $R _ { 1 }$. 
E)  Add 5 times $R _ { 2 }$ to $R _ { 1 }$. 
A)  Add 5 times $R _ { 1 }$ to $R _ { 2 }$. 
B)  Add $- 5$ times $R _ { 2 }$ to $R _ { 1 }$. 
C)  Add $- 5$ times $R _ { 1 }$ to $R _ { 2 }$. 
D)  Add 5 times $R _ { 1 }$ to $R _ { 1 }$. 
E)  Add 5 times $R _ { 2 }$ to $R _ { 1 }$.

Question 19

An augmented matrix that represents a system of linear equations (in variables $x , y$, and $z$ ) has been reduced using Gauss-Jordan elimination. Write the solution represented by the augmented matrix.
$$\left[ \begin{array} { c c c : c } 
1 & 0 & 0 & - 1 \
0 & 1 & 0 & 3 \
0 & 0 & 1 & 8
\end{array} \right]$$

Accepted Answer

A)  $x = - 1 , y = 3 , z = 8$ 
B)  $x = 1 , y = - 3 , z = - 8$ 
C)  $x = 0 , y = 0 , z = 0$ 
D)  $x = - x , y = 8 y , z = 3 z$ 
E)  $x = - 1 , y = 0 , z = 0$ 
A)  $x = - 1 , y = 3 , z = 8$ 
B)  $x = 1 , y = - 3 , z = - 8$ 
C)  $x = 0 , y = 0 , z = 0$ 
D)  $x = - x , y = 8 y , z = 3 z$ 
E)  $x = - 1 , y = 0 , z = 0$

Question 20

Solve system of equations by the method of substitution.
$$\left\{ \begin{aligned}
12 x ^ { 3 } - 9 y & = 0 \
12 x - y & = 0
\end{aligned} \right.$$

Accepted Answer

A)  $\quad ( 0,0 ) , ( - 3 , - 36 ) , ( 3,36 )$ 
B)  $\quad ( 0,0 ) , ( - 3,36 ) , ( 3,36 )$ 
C)  $\quad ( 0,0 ) , ( 3 , - 36 ) , ( 3,36 )$ 
D)  $\quad ( 0,0 ) , ( - 3,37 ) , ( 3,37 )$ 
E)  $\quad ( 0,0 ) , ( - 3 , - 35 ) , ( 3,35 )$ 
A)  $\quad ( 0,0 ) , ( - 3 , - 36 ) , ( 3,36 )$ 
B)  $\quad ( 0,0 ) , ( - 3,36 ) , ( 3,36 )$ 
C)  $\quad ( 0,0 ) , ( 3 , - 36 ) , ( 3,36 )$ 
D)  $\quad ( 0,0 ) , ( - 3,37 ) , ( 3,37 )$ 
E)  $\quad ( 0,0 ) , ( - 3 , - 35 ) , ( 3,35 )$

Solve system by the method of substitution and graph your solution. $\left\{ \begin{array} { l } y = x ^ { 3 } + 3 x ^ { 2 } + 2 x \\y = - x\end{array} \right.$

Given: $A = \left[ \begin{array} { r r r } 8 & - 7 & 0 \\ - 5 & - 2 & 3 \end{array} \right] , B = \left[ \begin{array} { r r r } 3 & 0 & 7 \\ 4 & 9 & - 2 \end{array} \right] , c = 8$ and $d = - 3$ , determine $c A + d B$ .

Find a system of linear equations that has the following solution. $\left( - \frac { 4 } { 7 } , 10 \right)$

Evaluate the expression. $\frac { 1 } { 4 } \left[ \begin{array} { l l l } - 9 & 1 & - 1\end{array} \right] + \left[ \begin{array} { l l l } - 4 & - 6 & 8\end{array} \right]$

Solve the system by the method of elimination. Round numbers to three decimal places. $\left\{ \begin{array} { c } 5.2 x + 8.1 y = 6.9 \\- 2.6 x + 1.1 y = - 0.7\end{array} \right.$

Solve the system of equations below using Gaussian elimination. 5x+4y+3z =54 x-2y+2z =36 x-y-z =-18

Solve system of equations by the method of substitution. $\left\{ \begin{array} { r } 15 x ^ { 3 } - 25 y = 0 \\15 x - y = 0\end{array} \right.$

Solve for X in the equation given. $9 A + 6 B = 3 X , A = \left[ \begin{array} { c c c } 6 & - 5 & 3 \\ 8 & - 3 & - 7 \end{array} \right]$ and $B = \left[ \begin{array} { c c c } 3 & 5 & - 1 \\ 1 & - 2 & 5 \end{array} \right]$

Find $| A B |$ , if $A = \left[ \begin{array} { r r r } - 3 & 4 & 5 \\- 3 & - 5 & 1 \\5 & - 5 & 1\end{array} \right] , B = \left[ \begin{array} { r r r } - 1 & - 2 & 5 \\4 & 1 & - 3 \\- 1 & - 1 & 4\end{array} \right]$

Use the matrix capabilities of a graphing utility to find the inverse of the matrix $\frac { 1 } { 6 } \left[ \begin{array} { c c c } - 4 & - 5 & 3 \\ - 4 & - 8 & 3 \\ 1 & 2 & 0 \end{array} \right]$ (if it exists).

Solve the system by the method of elimination. $\left\{ \begin{array} { c } \frac { 1 } { 9 } x - \frac { 1 } { 8 } y = 6 \\- 48 x + 54 y = - 2591\end{array} \right.$

Solve the system by the method of elimination. $\left\{ \begin{aligned}4 x + 5 y & = - 71 \\x - y & = - 2\end{aligned} \right.$

Solve the system of linear equations. $\left\{ \begin{array} { c } x + 5 y + 5 z = 9 \\- 2 x + z = - 6 \\2 x + 4 y - 3 z = - 2\end{array} \right.$

Solve the system of linear equations. $\left\{ \begin{aligned}x + y + z & = - 6 \\x - 6 y - 7 z & = 76 \\8 y - 6 z & = - 18\end{aligned} \right.$

Determine which ordered pair is a solution of the system. $\left\{ \begin{aligned}x - 2 y ^ { 2 } & = - 7 \\- 5 x + 6 y & = 7\end{aligned} \right.$

Identify the elementary row operation being performed to obtain the new rowequivalent matrix.

Solve system of equations by the method of substitution. $\left\{ \begin{aligned}12 x ^ { 3 } - 9 y & = 0 \\12 x - y & = 0\end{aligned} \right.$

Functions and Their Graphs

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Additional Topics in Trigonometry

Sequences, Series, and Probability

Topics in Analytic Geometry

Analytic Geometry in Three Dimensions

Limits and an Introduction to Calculus

Review of Graphs, Equations, and Inequalities

Filters

Exam 7: Linear Systems and Matrices

Solve system by the method of substitution and graph your solution. {y=x3+3x2+2xy=−x\left\{ \begin{array} { l } y = x ^ { 3 } + 3 x ^ { 2 } + 2 x \\y = - x\end{array} \right.{y=x3+3x2+2xy=−x​

Find a system of linear equations that has the following solution. (−47,10)\left( - \frac { 4 } { 7 } , 10 \right)(−74​,10)

Evaluate the expression. 14[−91−1]+[−4−68]\frac { 1 } { 4 } \left[ \begin{array} { l l l } - 9 & 1 & - 1\end{array} \right] + \left[ \begin{array} { l l l } - 4 & - 6 & 8\end{array} \right]41​[−9​1​−1​]+[−4​−6​8​]

Use a system of equations to find the specified equation that passes through the points. Solve the system using matrices. Parabola: y=ax2+bx+cy = a x ^ { 2 } + b x + cy=ax2+bx+c

Solve the system by the method of elimination. Round numbers to three decimal places. {5.2x+8.1y=6.9−2.6x+1.1y=−0.7\left\{ \begin{array} { c } 5.2 x + 8.1 y = 6.9 \\- 2.6 x + 1.1 y = - 0.7\end{array} \right.{5.2x+8.1y=6.9−2.6x+1.1y=−0.7​

Solve the system of equations below using Gaussian elimination. 5x+4y+3z =54 x-2y+2z =36 x-y-z =-18

Solve system of equations by the method of substitution. {15x3−25y=015x−y=0\left\{ \begin{array} { r } 15 x ^ { 3 } - 25 y = 0 \\15 x - y = 0\end{array} \right.{15x3−25y=015x−y=0​

Use the matrix capabilities of a graphing utility to find the inverse of the matrix 16[−4−53−4−83120]\frac { 1 } { 6 } \left[ \begin{array} { c c c } - 4 & - 5 & 3 \\ - 4 & - 8 & 3 \\ 1 & 2 & 0 \end{array} \right]61​​−4−41​−5−82​330​​ (if it exists).

Solve the system by the method of elimination. {19x−18y=6−48x+54y=−2591\left\{ \begin{array} { c } \frac { 1 } { 9 } x - \frac { 1 } { 8 } y = 6 \\- 48 x + 54 y = - 2591\end{array} \right.{91​x−81​y=6−48x+54y=−2591​

Solve the system by the method of elimination. {4x+5y=−71x−y=−2\left\{ \begin{aligned}4 x + 5 y & = - 71 \\x - y & = - 2\end{aligned} \right.{4x+5yx−y​=−71=−2​

Solve the system of linear equations. {x+5y+5z=9−2x+z=−62x+4y−3z=−2\left\{ \begin{array} { c } x + 5 y + 5 z = 9 \\- 2 x + z = - 6 \\2 x + 4 y - 3 z = - 2\end{array} \right.⎩⎨⎧​x+5y+5z=9−2x+z=−62x+4y−3z=−2​

Solve the system of linear equations. {x+y+z=−6x−6y−7z=768y−6z=−18\left\{ \begin{aligned}x + y + z & = - 6 \\x - 6 y - 7 z & = 76 \\8 y - 6 z & = - 18\end{aligned} \right.⎩⎨⎧​x+y+zx−6y−7z8y−6z​=−6=76=−18​

Determine which ordered pair is a solution of the system. {x−2y2=−7−5x+6y=7\left\{ \begin{aligned}x - 2 y ^ { 2 } & = - 7 \\- 5 x + 6 y & = 7\end{aligned} \right.{x−2y2−5x+6y​=−7=7​

Identify the elementary row operation being performed to obtain the new rowequivalent matrix.

Solve system of equations by the method of substitution. {12x3−9y=012x−y=0\left\{ \begin{aligned}12 x ^ { 3 } - 9 y & = 0 \\12 x - y & = 0\end{aligned} \right.{12x3−9y12x−y​=0=0​

Functions and Their Graphs

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Additional Topics in Trigonometry

Sequences, Series, and Probability

Topics in Analytic Geometry

Analytic Geometry in Three Dimensions

Limits and an Introduction to Calculus

Review of Graphs, Equations, and Inequalities

Filters

Solve system by the method of substitution and graph your solution. $\left\{ \begin{array} { l } y = x ^ { 3 } + 3 x ^ { 2 } + 2 x \\y = - x\end{array} \right.$

Find a system of linear equations that has the following solution. $\left( - \frac { 4 } { 7 } , 10 \right)$

Evaluate the expression. $\frac { 1 } { 4 } \left[ \begin{array} { l l l } - 9 & 1 & - 1\end{array} \right] + \left[ \begin{array} { l l l } - 4 & - 6 & 8\end{array} \right]$

Solve the system by the method of elimination. Round numbers to three decimal places. $\left\{ \begin{array} { c } 5.2 x + 8.1 y = 6.9 \\- 2.6 x + 1.1 y = - 0.7\end{array} \right.$

Solve system of equations by the method of substitution. $\left\{ \begin{array} { r } 15 x ^ { 3 } - 25 y = 0 \\15 x - y = 0\end{array} \right.$

Use the matrix capabilities of a graphing utility to find the inverse of the matrix $\frac { 1 } { 6 } \left[ \begin{array} { c c c } - 4 & - 5 & 3 \\ - 4 & - 8 & 3 \\ 1 & 2 & 0 \end{array} \right]$ (if it exists).

Solve the system by the method of elimination. $\left\{ \begin{array} { c } \frac { 1 } { 9 } x - \frac { 1 } { 8 } y = 6 \\- 48 x + 54 y = - 2591\end{array} \right.$

Solve the system by the method of elimination. $\left\{ \begin{aligned}4 x + 5 y & = - 71 \\x - y & = - 2\end{aligned} \right.$

Solve the system of linear equations. $\left\{ \begin{array} { c } x + 5 y + 5 z = 9 \\- 2 x + z = - 6 \\2 x + 4 y - 3 z = - 2\end{array} \right.$

Solve the system of linear equations. $\left\{ \begin{aligned}x + y + z & = - 6 \\x - 6 y - 7 z & = 76 \\8 y - 6 z & = - 18\end{aligned} \right.$

Determine which ordered pair is a solution of the system. $\left\{ \begin{aligned}x - 2 y ^ { 2 } & = - 7 \\- 5 x + 6 y & = 7\end{aligned} \right.$

Solve system of equations by the method of substitution. $\left\{ \begin{aligned}12 x ^ { 3 } - 9 y & = 0 \\12 x - y & = 0\end{aligned} \right.$