Question 1

Provide an appropriate response.
-For a certain system of two linear equations, the solution set is $\{ - 9,5 \}$, and $D = 9$. Find the values of $D _ { x }$ and $D _ { y }$.

Accepted Answer

A)  $\mathrm { D } _ { \mathrm { X } } = - 1 ; \mathrm { D } _ { \mathrm { y } } = \frac { 5 } { 9 }$ 
B)  $\mathrm { D } _ { \mathrm { x } } = 45 ; \mathrm { D } _ { \mathrm { y } } = - 81$ 
C)  $\mathrm { D } _ { \mathrm { x } } = - 81 ; \mathrm { D } _ { \mathrm { y } } = 45$ 
D)  $D _ { \mathrm { X } } = - 9 ; \mathrm { D } _ { \mathrm { y } } = 5$ 
A)  $\mathrm { D } _ { \mathrm { X } } = - 1 ; \mathrm { D } _ { \mathrm { y } } = \frac { 5 } { 9 }$ 
B)  $\mathrm { D } _ { \mathrm { x } } = 45 ; \mathrm { D } _ { \mathrm { y } } = - 81$ 
C)  $\mathrm { D } _ { \mathrm { x } } = - 81 ; \mathrm { D } _ { \mathrm { y } } = 45$ 
D)  $D _ { \mathrm { X } } = - 9 ; \mathrm { D } _ { \mathrm { y } } = 5$

Question 2

Use Cramerʹs rule to solve the system of equations. If D = 0, use another method to determine the solution set.
-$$\begin{array} { l } 
9 x + 6 y = - 6 \
- 5 x + 3 y = - 3
\end{array}$$

Accepted Answer

A)  $\{ ( 0 , - 1 ) \}$ 
B)  $\{ ( - 1,0 ) \}$ 
C)  Cramer's rule does not apply since $\mathrm { D } = 0$; 
D)  $\{ ( 0,0 ) \}$ 
A)  $\{ ( 0 , - 1 ) \}$ 
B)  $\{ ( - 1,0 ) \}$ 
C)  Cramer's rule does not apply since $\mathrm { D } = 0$; 
D)  $\{ ( 0,0 ) \}$

Question 3

Solve the problem.
-Given $A = \left[ \begin{array} { r r r } 0 & - 1 & 0 \ 0 & 1 & 1 \ - 1 & 0 & 1 \end{array} \right]$ and $B = \left[ \begin{array} { r r r } - 1 & - 1 & 0 \ 0 & 1 & 0 \ - 1 & 1 & 0 \end{array} \right]$, find $A B$ and $B A$.

Accepted Answer

A) 
$\mathrm { AB } = \left[ \begin{array} { r r r } 0 & 1 & 0 \ - 1 & 0 & 0 \ 0 & 2 & 0 \end{array} \right] ; \mathrm { BA } = \left[ \begin{array} { c r c } 0 & 2 & 1 \ 0 & - 1 & - 1 \ 0 & 0 & - 1 \end{array} \right]$ 
B) 
$\mathrm { AB } = \left[ \begin{array} { r r r } 0 & - 1 & 0 \ - 1 & 2 & 0 \ 0 & 2 & 0 \end{array} \right] ; \mathrm { BA } = \left[ \begin{array} { l l l } 0 & 0 & - 1 \ 0 & 1 & 1 \ 0 & 2 & 1 \end{array} \right]$ 
C) 
$\mathrm { AB } = \left[ \begin{array} { l l l } 0 & 1 & 0 \ 0 & 1 & 0 \ 1 & 0 & 0 \end{array} \right] ; \mathrm { BA } = \left[ \begin{array} { l l l } 0 & 1 & 0 \ 0 & 1 & 0 \ 1 & 0 & 0 \end{array} \right]$ 
D) 
$\mathrm { AB } = \left[ \begin{array} { l l l } 0 & 0 & - 1 \ 0 & 1 & 1 \ 0 & 2 & 1 \end{array} \right] ; \mathrm { BA } = \left[ \begin{array} { r r r } 0 & - 1 & 0 \ - 1 & 2 & 0 \ 0 & 2 & 0 \end{array} \right]$ 
A) 
$\mathrm { AB } = \left[ \begin{array} { r r r } 0 & 1 & 0 \ - 1 & 0 & 0 \ 0 & 2 & 0 \end{array} \right] ; \mathrm { BA } = \left[ \begin{array} { c r c } 0 & 2 & 1 \ 0 & - 1 & - 1 \ 0 & 0 & - 1 \end{array} \right]$ 
B) 
$\mathrm { AB } = \left[ \begin{array} { r r r } 0 & - 1 & 0 \ - 1 & 2 & 0 \ 0 & 2 & 0 \end{array} \right] ; \mathrm { BA } = \left[ \begin{array} { l l l } 0 & 0 & - 1 \ 0 & 1 & 1 \ 0 & 2 & 1 \end{array} \right]$ 
C) 
$\mathrm { AB } = \left[ \begin{array} { l l l } 0 & 1 & 0 \ 0 & 1 & 0 \ 1 & 0 & 0 \end{array} \right] ; \mathrm { BA } = \left[ \begin{array} { l l l } 0 & 1 & 0 \ 0 & 1 & 0 \ 1 & 0 & 0 \end{array} \right]$ 
D) 
$\mathrm { AB } = \left[ \begin{array} { l l l } 0 & 0 & - 1 \ 0 & 1 & 1 \ 0 & 2 & 1 \end{array} \right] ; \mathrm { BA } = \left[ \begin{array} { r r r } 0 & - 1 & 0 \ - 1 & 2 & 0 \ 0 & 2 & 0 \end{array} \right]$

Question 4

Solve the problem.
-Find the equation of the parabola $y = a x ^ { 2 } + b x + c$ that passes through the points $( - 2,0 ) , ( 0 , - 4 )$, and $( 3,3 )$.

Accepted Answer

A)  $y = - \frac { 7 } { 15 } x ^ { 2 } - \frac { 4 } { 15 } x - 7$ 
B)  $y = \frac { 1 } { 5 } x ^ { 2 } - \frac { 8 } { 15 } x - \frac { 4 } { 3 }$ 
C)  $y = \frac { 13 } { 15 } x ^ { 2 } - \frac { 4 } { 15 } x - 4$ 
D)  $y = - \frac { 4 } { 15 } x ^ { 2 } + \frac { 13 } { 15 } x - 4$ 
A)  $y = - \frac { 7 } { 15 } x ^ { 2 } - \frac { 4 } { 15 } x - 7$ 
B)  $y = \frac { 1 } { 5 } x ^ { 2 } - \frac { 8 } { 15 } x - \frac { 4 } { 3 }$ 
C)  $y = \frac { 13 } { 15 } x ^ { 2 } - \frac { 4 } { 15 } x - 4$ 
D)  $y = - \frac { 4 } { 15 } x ^ { 2 } + \frac { 13 } { 15 } x - 4$

Question 5

A triangle with vertices at (x1, y1), (x2, y2), and (x3, y3) has area equal to the absolute value of D, where $$D = \frac { 1 } { 2 } \left| \begin{array} { l l l } 
x _ { 1 } & y _ { 1 } & 1 \
x _ { 2 } & y _ { 2 } & 1 \
x _ { 3 } & y _ { 3 } & 1
\end{array} \right|$$ Find the area of the triangle having vertices at P, Q, and R.
-$\mathrm { P } ( - 3 , - 3 ) , \mathrm { Q } ( 0,5 ) , \mathrm { R } ( 4,2 )$

Accepted Answer

A)  38 
B)  41 
C)  0 
D)  $\frac { 41 } { 2 }$ 
A)  38 
B)  41 
C)  0 
D)  $\frac { 41 } { 2 }$

Question 6

Find the partial fraction decomposition for the rational expression.
-$\frac { 560 x ^ { 2 } + 320 x } { \left( x ^ { 2 } + 4 \right) ( x + 6 ) }$

Accepted Answer

A)  $\frac { 104 x + 456 } { x ^ { 2 } + 4 } + \frac { - 304 } { x + 6 }$ 
B)  $\frac { 104 x } { x + 6 } + \frac { 152 } { x ^ { 2 } + 4 }$ 
C)  $\frac { 104 x - 304 } { x ^ { 2 } + 4 } + \frac { - 456 } { x + 6 }$ 
D)  $\frac { 104 x - 304 } { x ^ { 2 } + 4 } + \frac { 456 } { x + 6 }$ 
A)  $\frac { 104 x + 456 } { x ^ { 2 } + 4 } + \frac { - 304 } { x + 6 }$ 
B)  $\frac { 104 x } { x + 6 } + \frac { 152 } { x ^ { 2 } + 4 }$ 
C)  $\frac { 104 x - 304 } { x ^ { 2 } + 4 } + \frac { - 456 } { x + 6 }$ 
D)  $\frac { 104 x - 304 } { x ^ { 2 } + 4 } + \frac { 456 } { x + 6 }$

Question 7

Determine the inequality which matches the calculator graph. Do not use your calculator. Instead, use your knowledge
of the concepts involved in graphing inequalities.
-

Accepted Answer

A)  $x \leq 2$ 
B)  $x \geq 2$ 
C)  $y \leq 2$ 
D)  $\mathrm { y } \geq 2$ 
A)  $x \leq 2$ 
B)  $x \geq 2$ 
C)  $y \leq 2$ 
D)  $\mathrm { y } \geq 2$

Question 8

Perform the operation or operations when possible.
-$$\left[ \begin{array} { r r } 
- 1 & 0 \
3 & 3
\end{array} \right] - \left[ \begin{array} { r r } 
- 1 & 3 \
3 & 1
\end{array} \right]$$

Accepted Answer

A) 
$\left[ \begin{array} { r r } 0 & 3 \ 0 & - 2 \end{array} \right]$ 
B) 
$\left[ \begin{array} { r r } - 2 & 3 \ 6 & 4 \end{array} \right]$ 
C) 
$\left[ \begin{array} { r r } 0 & - 3 \ 0 & 2 \end{array} \right]$ 
D) 
$[ - 1 ]$ 
A) 
$\left[ \begin{array} { r r } 0 & 3 \ 0 & - 2 \end{array} \right]$ 
B) 
$\left[ \begin{array} { r r } - 2 & 3 \ 6 & 4 \end{array} \right]$ 
C) 
$\left[ \begin{array} { r r } 0 & - 3 \ 0 & 2 \end{array} \right]$ 
D) 
$[ - 1 ]$

Question 9

Use the given row transformation to change the matrix as indicated.
-$\left[\begin{array}{rrr}
6 & 5 & 6 \
5 & -2 & 7 \
5 & 3 & 1
\end{array}\right] ;-6 \text { times row } 3 \text { added to row } 1$

Accepted Answer

A) 
$\left[\begin{array}{rrr}
6 & 5 & 1 \
5 & -2 & 7 \
-30 & -18 & -6
\end{array}\right]$ 
B) 
$\left[\begin{array}{ccr}
6 & 5 & 6 \
-25 & -20 & 1 \
-30 & -18 & -6
\end{array}\right]$ 
C) 
$\left[\begin{array}{rrr}
11 & 8 & 0 \
5 & -2 & 7 \
5 & 3 & 1
\end{array}\right]$ 
D) 
$\left[\begin{array}{ccc}
-24 & -13 & 0 \
5 & -2 & 7 \
5 & 3 & 1
\end{array}\right]$ 
A) 
$\left[\begin{array}{rrr}
6 & 5 & 1 \
5 & -2 & 7 \
-30 & -18 & -6
\end{array}\right]$ 
B) 
$\left[\begin{array}{ccr}
6 & 5 & 6 \
-25 & -20 & 1 \
-30 & -18 & -6
\end{array}\right]$ 
C) 
$\left[\begin{array}{rrr}
11 & 8 & 0 \
5 & -2 & 7 \
5 & 3 & 1
\end{array}\right]$ 
D) 
$\left[\begin{array}{ccc}
-24 & -13 & 0 \
5 & -2 & 7 \
5 & 3 & 1
\end{array}\right]$

Question 10

Give all solutions of the nonlinear system of equations, including those with nonreal complex components.
-$$\begin{array} { l } 
x y = 1 \
5 x - y = 4
\end{array}$$

Accepted Answer

A)  $\left\{ \left( - \frac { 1 } { 5 } , - 5 \right) \right\}$ 
B)  $\left\{ ( 1,1 ) , \left( - 5 , - \frac { 1 } { 5 } \right) \right\}$ 
C)  $\{ ( - 1,1 ) , ( 5 , - 5 ) \}$ 
D)  $\left\{ ( 1,1 ) , \left( - \frac { 1 } { 5 } , - 5 \right) \right\}$ 
A)  $\left\{ \left( - \frac { 1 } { 5 } , - 5 \right) \right\}$ 
B)  $\left\{ ( 1,1 ) , \left( - 5 , - \frac { 1 } { 5 } \right) \right\}$ 
C)  $\{ ( - 1,1 ) , ( 5 , - 5 ) \}$ 
D)  $\left\{ ( 1,1 ) , \left( - \frac { 1 } { 5 } , - 5 \right) \right\}$

Question 11

Solve the problem.
-The following table shows the per capita cumquat consumption, in pounds, in the Virgin Islands in three different years. Find a function of the form $f ( x ) = a x ^ { 2 } + b x + c$ that fits this data. Using this function, what would you predict the per capita cumquat consumption to be in year 12 ?

Accepted Answer

A)  $65.2 \mathrm { lb }$ 
B)  $65.6 \mathrm { lb }$ 
C)  $66.7 \mathrm { lb }$ 
D)  $62.9 \mathrm { lb }$ 
A)  $65.2 \mathrm { lb }$ 
B)  $65.6 \mathrm { lb }$ 
C)  $66.7 \mathrm { lb }$ 
D)  $62.9 \mathrm { lb }$

Question 12

Use the Gauss-Jordan method to solve the system of equations. If the system has infinitely many solutions, let the last
variable be the arbitrary variable.
-$$\begin{array} { l } 
x + 3 y - 2 z - w = 17 \
4 x + y + z + 2 w = 11 \
- 3 x - y - 3 z - 2 w = - 1 \
x - y - 3 z - 2 w = 7
\end{array}$$

Accepted Answer

A)  $\{ ( 17,11 , - 1,7 ) \}$ 
B)  $\{ ( 1,5 , - 8,4 ) \}$ 
C)  $\{ ( 2 + \mathrm { w } , 3 - 2 \mathrm { w } , - 4 + 2 \mathrm { w } , \mathrm { w } ) \}$ 
D)  $\{ ( 2,3 , - 4,2 ) \}$ 
A)  $\{ ( 17,11 , - 1,7 ) \}$ 
B)  $\{ ( 1,5 , - 8,4 ) \}$ 
C)  $\{ ( 2 + \mathrm { w } , 3 - 2 \mathrm { w } , - 4 + 2 \mathrm { w } , \mathrm { w } ) \}$ 
D)  $\{ ( 2,3 , - 4,2 ) \}$

Question 13

Find the inverse, if it exists, for the matrix.
-$$\left[ \begin{array} { l l } 
- 6 & - 6 \
- 4 & - 4
\end{array} \right]$$

Accepted Answer

A) 
$$\left[ \begin{array} { l } 
- \frac { 1 } { 5 } - \frac { 3 } { 10 } \
- \frac { 1 } { 5 } - \frac { 3 } { 10 }
\end{array} \right]$$ 
B)  The inverse does not exist. 
C) 
$$\left[ \begin{array} { r r } 
- \frac { 1 } { 5 } & \frac { 3 } { 10 } \
\frac { 1 } { 5 } & - \frac { 3 } { 10 }
\end{array} \right]$$ 
D) 
  
A) 
$$\left[ \begin{array} { l } 
- \frac { 1 } { 5 } - \frac { 3 } { 10 } \
- \frac { 1 } { 5 } - \frac { 3 } { 10 }
\end{array} \right]$$ 
B)  The inverse does not exist. 
C) 
$$\left[ \begin{array} { r r } 
- \frac { 1 } { 5 } & \frac { 3 } { 10 } \
\frac { 1 } { 5 } & - \frac { 3 } { 10 }
\end{array} \right]$$ 
D)

Question 14

Which method should be used to solve the system? Explain your answer, including a description of the first step.
-$$\begin{array} { l } 
x ^ { 2 } - 5 y ^ { 2 } = 100 \
- 4 x ^ { 2 } + 7 y ^ { 2 } = 81
\end{array}$$

Accepted Answer

Either method may be used. Elimination m

Question 15

Evaluate the determinant.
-$\left| \begin{array} { l l l } 6 & 2 & 3 \ 8 & 4 & 4 \ 5 & 9 & 3 \end{array} \right|$

Accepted Answer

A)  $- 76$ 
B)  4 
C)  $- 4$ 
D)  652 
A)  $- 76$ 
B)  4 
C)  $- 4$ 
D)  652

Question 16

A nonlinear system is given, along with the graphs of both equations in the system. Determine if the points of
intersection specified on the graph are solutions of the system by substituting directly into both equations.
-$\begin{array}{l}
y=\ln x \
x^{2}-y^{2}=7
\end{array}$

Accepted Answer

A)  Yes 
B)  $\mathrm { No }$ 
A)  Yes 
B)  $\mathrm { No }$

Question 17

Write the augmented matrix for the system. Do not solve the system.
-$$\begin{array} { r } 
3 x + 9 z - 78 = 0 \
7 y + 5 z - 54 = 0 \
4 x + 8 y + 7 z - 80 = 0
\end{array}$$

Accepted Answer

A) 
$\left[ \begin{array} { l l l | l } 3 & 9 & 0 & 78 \ 7 & 5 & 0 & 54 \ 4 & 8 & 7 & 80 \end{array} \right]$ 
B) 
$\left[ \begin{array} { l l l } 3 & 0 & 9 \ 0 & 7 & 5 \ 4 & 8 & 7 \end{array} \right]$ 
C) 
$\left[ \begin{array} { l l l | l } 3 & 0 & 4 & 78 \ 0 & 7 & 8 & 54 \ 9 & 5 & 7 & 80 \end{array} \right]$ 
D) 
$\left[ \begin{array} { l l l | l } 3 & 0 & 9 & 78 \ 0 & 7 & 5 & 54 \ 4 & 8 & 7 & 80 \end{array} \right]$ 
A) 
$\left[ \begin{array} { l l l | l } 3 & 9 & 0 & 78 \ 7 & 5 & 0 & 54 \ 4 & 8 & 7 & 80 \end{array} \right]$ 
B) 
$\left[ \begin{array} { l l l } 3 & 0 & 9 \ 0 & 7 & 5 \ 4 & 8 & 7 \end{array} \right]$ 
C) 
$\left[ \begin{array} { l l l | l } 3 & 0 & 4 & 78 \ 0 & 7 & 8 & 54 \ 9 & 5 & 7 & 80 \end{array} \right]$ 
D) 
$\left[ \begin{array} { l l l | l } 3 & 0 & 9 & 78 \ 0 & 7 & 5 & 54 \ 4 & 8 & 7 & 80 \end{array} \right]$

Question 18

Graph the solution set of the system of inequalities.
-

Accepted Answer

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

Question 19

Solve the system for x and y using Cramerʹs rule. Assume a and b are nonzero constants.
-$$\begin{array} { l } 
x + b y = a ^ { 2 } \
a x + y = b ^ { 2 }
\end{array}$$

Accepted Answer

A)  $\left\{ \left( \frac { a ^ { 2 } - b ^ { 3 } } { a + b } , \frac { a ^ { 2 } - b ^ { 3 } } { a + b } \right) \right\}$ 
B)  $\left\{ \left( \frac { a ^ { 2 } - b ^ { 3 } } { 1 - a b } , \frac { b ^ { 2 } - a ^ { 3 } } { 1 - a b } \right) \right\}$ 
C)  $\left\{ \left( - \frac { a ^ { 2 } - b ^ { 3 } } { a b } , - \frac { b ^ { 2 } - a ^ { 3 } } { a b } \right) \right\}$ 
D)  $\left\{ \left( \frac { b ^ { 3 } } { 1 - a b } , \frac { a ^ { 3 } } { 1 - a b } \right) \right\}$ 
A)  $\left\{ \left( \frac { a ^ { 2 } - b ^ { 3 } } { a + b } , \frac { a ^ { 2 } - b ^ { 3 } } { a + b } \right) \right\}$ 
B)  $\left\{ \left( \frac { a ^ { 2 } - b ^ { 3 } } { 1 - a b } , \frac { b ^ { 2 } - a ^ { 3 } } { 1 - a b } \right) \right\}$ 
C)  $\left\{ \left( - \frac { a ^ { 2 } - b ^ { 3 } } { a b } , - \frac { b ^ { 2 } - a ^ { 3 } } { a b } \right) \right\}$ 
D)  $\left\{ \left( \frac { b ^ { 3 } } { 1 - a b } , \frac { a ^ { 3 } } { 1 - a b } \right) \right\}$

Question 20

Write the system of equations associated with the augmented matrix. Do not solve.
-$\left[ \begin{array} { r r r | r } - 8 & 9 & 8 & 5 \ 5 & - 6 & 0 & 8 \ - 8 & 0 & - 3 & - 3 \end{array} \right]$

Accepted Answer

A) 
$\begin{array}{l}
-8 x+9 y+8 z=5 \
5 x-6 y=8 \
-8 x-3 y=-3
\end{array}$ 
B)  $\begin{array}{cc}
-8 x+9 y+8 z=5 \
5 x-6 y & =8 \
-8 x-3 z=-3
\end{array}$ 
C)  
$\begin{array}{c}
-8 x+9 y+8 z=5 \
5 x-6 y+8 z=0 \
-8 x-3 y-3 z=0
\end{array}$

D
$\begin{aligned}
-8 x+9 y+8 z &=5 \
5 x+-6 z &=8 \
-8 x-3 y &=-3
\end{aligned}$ 
A) 
$\begin{array}{l}
-8 x+9 y+8 z=5 \
5 x-6 y=8 \
-8 x-3 y=-3
\end{array}$ 
B)  $\begin{array}{cc}
-8 x+9 y+8 z=5 \
5 x-6 y & =8 \
-8 x-3 z=-3
\end{array}$ 
C)  
$\begin{array}{c}
-8 x+9 y+8 z=5 \
5 x-6 y+8 z=0 \
-8 x-3 y-3 z=0
\end{array}$

D
$\begin{aligned}
-8 x+9 y+8 z &=5 \
5 x+-6 z &=8 \
-8 x-3 y &=-3
\end{aligned}$

Provide an appropriate response. -For a certain system of two linear equations, the solution set is $\{ - 9,5 \}$ , and $D = 9$ . Find the values of $D _ { x }$ and $D _ { y }$ .

Use Cramerʹs rule to solve the system of equations. If D = 0, use another method to determine the solution set. - 9x+6y=-6 -5x+3y=-3

Solve the problem. -Given $A = \left[ \begin{array} { r r r } 0 & - 1 & 0 \\ 0 & 1 & 1 \\ - 1 & 0 & 1 \end{array} \right]$ and $B = \left[ \begin{array} { r r r } - 1 & - 1 & 0 \\ 0 & 1 & 0 \\ - 1 & 1 & 0 \end{array} \right]$ , find $A B$ and $B A$ .

Solve the problem. -Find the equation of the parabola $y = a x ^ { 2 } + b x + c$ that passes through the points $( - 2,0 ) , ( 0 , - 4 )$ , and $( 3,3 )$ .

Find the partial fraction decomposition for the rational expression. - $\frac { 560 x ^ { 2 } + 320 x } { \left( x ^ { 2 } + 4 \right) ( x + 6 ) }$

Determine the inequality which matches the calculator graph. Do not use your calculator. Instead, use your knowledge of the concepts involved in graphing inequalities. -

Perform the operation or operations when possible. - $\left[ \begin{array} { r r } - 1 & 0 \\3 & 3\end{array} \right] - \left[ \begin{array} { r r } - 1 & 3 \\3 & 1\end{array} \right]$

Use the given row transformation to change the matrix as indicated. - $\left[\begin{array}{rrr}6 & 5 & 6 \\5 & -2 & 7 \\5 & 3 & 1\end{array}\right] ;-6 \text { times row } 3 \text { added to row } 1$

Give all solutions of the nonlinear system of equations, including those with nonreal complex components. - xy=1 5x-y=4

Use the Gauss-Jordan method to solve the system of equations. If the system has infinitely many solutions, let the last variable be the arbitrary variable. - x+3y-2z-w=17 4x+y+z+2w=11 -3x-y-3z-2w=-1 x-y-3z-2w=7

Find the inverse, if it exists, for the matrix. - $\left[ \begin{array} { l l } - 6 & - 6 \\- 4 & - 4\end{array} \right]$

Which method should be used to solve the system? Explain your answer, including a description of the first step. - -5=100 -4+7=81

Evaluate the determinant. - $\left| \begin{array} { l l l } 6 & 2 & 3 \\ 8 & 4 & 4 \\ 5 & 9 & 3 \end{array} \right|$

Write the augmented matrix for the system. Do not solve the system. - 3x+9z-78=0 7y+5z-54=0 4x+8y+7z-80=0

Graph the solution set of the system of inequalities. -

Solve the system for x and y using Cramerʹs rule. Assume a and b are nonzero constants. - x+by= ax+y=

Write the system of equations associated with the augmented matrix. Do not solve. - $\left[ \begin{array} { r r r | r } - 8 & 9 & 8 & 5 \\ 5 & - 6 & 0 & 8 \\ - 8 & 0 & - 3 & - 3 \end{array} \right]$

Equations and Inequalities

Graphs and Functions

Polynomial and Rational Functions

Inverse, Exponential, and Logarithmic Functions

Trigonometric Functions

The Circular Functions and Their Graphs

Trigonometric Identities and Equations

Applications of Trigonometry

Analytic Geometry

Further Topics in Algebra

Review of Basic Concepts

Filters

Exam 9: Systems and Matrices

Provide an appropriate response. -For a certain system of two linear equations, the solution set is {−9,5}\{ - 9,5 \}{−9,5} , and D=9D = 9D=9 . Find the values of DxD _ { x }Dx​ and DyD _ { y }Dy​ .