Question 1

Find the solution set of the system. $$\left\{ \begin{array} { l } 
y < 5 x + 4 \
y < - 4 x + 5
\end{array} \right.$$

Accepted Answer

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

Question 2

Solve the system using Gaussian elimination. If $( x , y )$ is the solution to the system, give the value of $2 x - y$.
$$\left\{ \begin{array} { c } 
x + y = 24 \
x - 2 y = - 3
\end{array} \right.$$

Accepted Answer

A)  $\quad 19$ 
B)  $\quad 20$ 
C)  21 
D)  24 
E)  $\quad 18$ 
A)  $\quad 19$ 
B)  $\quad 20$ 
C)  21 
D)  24 
E)  $\quad 18$

Question 3

Use Cramer's rule to find the solution of the system, if possible. $$\left\{ \begin{array} { c } 
x - y - z = 2 \
x + y + z = 18 \
- x - y + z = - 12
\end{array} \right.$$

Accepted Answer

A)  $\quad x = 3 , y = 5 , z = 10$ 
B)  $\quad x = 5 , y = 10 , z = 3$ 
C)  $x = 10 , y = 5 , z = 3$ 
D)  The system is inconsistent. 
E)  The equations are dependent. 
A)  $\quad x = 3 , y = 5 , z = 10$ 
B)  $\quad x = 5 , y = 10 , z = 3$ 
C)  $x = 10 , y = 5 , z = 3$ 
D)  The system is inconsistent. 
E)  The equations are dependent.

Question 4

Find values of x and y, if any, that will make the matrices equal. $$\left[ \begin{array} { l l } 
x & y \
1 & 6
\end{array} \right] = \left[ \begin{array} { l l } 
2 & 9 \
1 & 6
\end{array} \right]$$

Accepted Answer

A)  $\quad x = - 2 , y = 9$ 
B)  $\quad x = 2 , y = 9$ 
C)  $\quad x = - 2 , y = - 9$ 
D)  $\quad x = 9 , y = 2$ 
E)  no solution 
A)  $\quad x = - 2 , y = 9$ 
B)  $\quad x = 2 , y = 9$ 
C)  $\quad x = - 2 , y = - 9$ 
D)  $\quad x = 9 , y = 2$ 
E)  no solution

Question 5

Find the graph of the linear inequality. $3 y \geq 2 x - 9$

Accepted Answer

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

Question 6

Evaluate the determinant. $\left| \begin{array} { c c } 8 & 10 \ - 8 & 4 \end{array} \right|$

Accepted Answer

A)  $\quad D = 2,560$ 
B)  $\quad D = 112$ 
C)  $\quad D = - 117$ 
D)  $\quad D = - 112$ 
E)  $\quad D = - 48$ 
A)  $\quad D = 2,560$ 
B)  $\quad D = 112$ 
C)  $\quad D = - 117$ 
D)  $\quad D = - 112$ 
E)  $\quad D = - 48$

Question 7

Decompose the fraction into partial fractions. $$\frac { 9 x ^ { 2 } + 8 x + 9 } { x ^ { 3 } + x }$$

Accepted Answer

A)  $\quad \frac { 8 } { x } - \frac { 9 } { x ^ { 2 } + 1 }$ 
B)  $\quad \frac { 9 } { x } - \frac { 8 } { x ^ { 2 } + 1 }$ 
C)  $\frac { 8 } { x } + \frac { 9 } { x ^ { 2 } + 1 }$ 
D)  $\frac { 9 } { x } + \frac { 8 } { x ^ { 2 } + 1 }$ 
E)  none of these 
A)  $\quad \frac { 8 } { x } - \frac { 9 } { x ^ { 2 } + 1 }$ 
B)  $\quad \frac { 9 } { x } - \frac { 8 } { x ^ { 2 } + 1 }$ 
C)  $\frac { 8 } { x } + \frac { 9 } { x ^ { 2 } + 1 }$ 
D)  $\frac { 9 } { x } + \frac { 8 } { x ^ { 2 } + 1 }$ 
E)  none of these

Question 8

Find the graph of the linear inequality. $$2 x - 4 y > 2$$

Accepted Answer

A) 
  
B) 
  
C) 
 
$\mathrm { d }$.
  
A) 
  
B) 
  
C) 
 
$\mathrm { d }$.

Question 9

Find the solution set of the system. $\left\{ \begin{array} { l } 
y \leq - 4 \
x > - 4
\end{array} \right.$

Accepted Answer

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

Question 10

Find the inverse of the matrix. $$\left[ \begin{array} { c c c } 
32 & 1 & - 1 \
32 & 32 & - 1 \
- 1 & - 1 & 1
\end{array} \right]$$

Accepted Answer

A)  $\left[ \begin{array} { c c c } - \frac { 1 } { 31 } & 0 & \frac { 1 } { 31 } \ \frac { 1 } { 31 } & \frac { 1 } { 31 } & 0 \ 0 & \frac { 1 } { 31 } & \frac { 32 } { 31 } \end{array} \right]$ 
B)  $\left[ \begin{array} { c c c } \frac { 1 } { 31 } & 0 & \frac { 1 } { 31 } \ - \frac { 1 } { 31 } & \frac { 1 } { 31 } & 0 \ 0 & \frac { 1 } { 31 } & \frac { 32 } { 31 } \end{array} \right]$ 
C) 
$$\left[ \begin{array} { c c c } 
\frac { 1 } { 31 } & 0 & \frac { 1 } { 31 } \
\frac { 1 } { 31 } & - \frac { 1 } { 31 } & 0 \
0 & \frac { 1 } { 31 } & \frac { 32 } { 31 }
\end{array} \right]$$ 
D)  $\left[ \begin{array} { c c c } \frac { 1 } { 31 } & 1 & \frac { 1 } { 31 } \ - \frac { 1 } { 31 } & \frac { 1 } { 31 } & 0 \ 25 & \frac { 1 } { 31 } & \frac { 32 } { 31 } \end{array} \right]$ 
E)  $\left[ \begin{array} { c c c } - \frac { 1 } { 31 } & 0 & \frac { 1 } { 31 } \ - \frac { 1 } { 31 } & \frac { 1 } { 31 } & 0 \ 0 & \frac { 1 } { 31 } & \frac { 32 } { 31 } \end{array} \right]$ 
A)  $\left[ \begin{array} { c c c } - \frac { 1 } { 31 } & 0 & \frac { 1 } { 31 } \ \frac { 1 } { 31 } & \frac { 1 } { 31 } & 0 \ 0 & \frac { 1 } { 31 } & \frac { 32 } { 31 } \end{array} \right]$ 
B)  $\left[ \begin{array} { c c c } \frac { 1 } { 31 } & 0 & \frac { 1 } { 31 } \ - \frac { 1 } { 31 } & \frac { 1 } { 31 } & 0 \ 0 & \frac { 1 } { 31 } & \frac { 32 } { 31 } \end{array} \right]$ 
C) 
$$\left[ \begin{array} { c c c } 
\frac { 1 } { 31 } & 0 & \frac { 1 } { 31 } \
\frac { 1 } { 31 } & - \frac { 1 } { 31 } & 0 \
0 & \frac { 1 } { 31 } & \frac { 32 } { 31 }
\end{array} \right]$$ 
D)  $\left[ \begin{array} { c c c } \frac { 1 } { 31 } & 1 & \frac { 1 } { 31 } \ - \frac { 1 } { 31 } & \frac { 1 } { 31 } & 0 \ 25 & \frac { 1 } { 31 } & \frac { 32 } { 31 } \end{array} \right]$ 
E)  $\left[ \begin{array} { c c c } - \frac { 1 } { 31 } & 0 & \frac { 1 } { 31 } \ - \frac { 1 } { 31 } & \frac { 1 } { 31 } & 0 \ 0 & \frac { 1 } { 31 } & \frac { 32 } { 31 } \end{array} \right]$

Question 11

Solve the system by the addition method, if possible. If a solution exists, give the value of x. $\left\{ \begin{array} { l } 
4 ( x + y ) = y + 17 \
7 ( x + 1 ) = y + 18
\end{array} \right.$

Accepted Answer

A) 2 
B) 5 
C)  4 
D)  $- 1$ 
E)  no solution 
A) 2 
B) 5 
C)  4 
D)  $- 1$ 
E)  no solution

Question 12

Illustration shows three circles traced out by a figure skater during her performance.If the centers of the circles are the given distances apart, find the radius of each circle.  
$A = 10 , B = 18 , C = 20$

Accepted Answer

A)  $\quad r _ { 1 } = 4 , r _ { 2 } = 6 , r _ { 3 } = 14$ 
B)  $\quad r _ { 1 } = 3 , r _ { 2 } = 6 , r _ { 3 } = 15$ 
C)  $\quad r _ { 1 } = 4 , r _ { 2 } = 14 , r _ { 3 } = 6$ 
D)  $\quad r _ { 1 } = 14 , r _ { 2 } = 4 , r _ { 3 } = 6$ 
E)  $\quad r _ { 1 } = 6 , r _ { 2 } = 14 , r _ { 3 } = 4$ 
A)  $\quad r _ { 1 } = 4 , r _ { 2 } = 6 , r _ { 3 } = 14$ 
B)  $\quad r _ { 1 } = 3 , r _ { 2 } = 6 , r _ { 3 } = 15$ 
C)  $\quad r _ { 1 } = 4 , r _ { 2 } = 14 , r _ { 3 } = 6$ 
D)  $\quad r _ { 1 } = 14 , r _ { 2 } = 4 , r _ { 3 } = 6$ 
E)  $\quad r _ { 1 } = 6 , r _ { 2 } = 14 , r _ { 3 } = 4$

Question 13

What is element $a _ { 11 }$ of the inverse of the following matrix?
$$\left[ \begin{array} { c c } 
16 & 1 \
1 & 8
\end{array} \right]$$

Accepted Answer

A)  $\frac { 8 } { 257 }$ 
B)  $\frac { 8 } { 127 }$ 
C)  $- \frac { 16 } { 127 }$ 
D)  $- \frac { 8 } { 127 }$ 
E)  $\frac { 16 } { 127 }$ 
A)  $\frac { 8 } { 257 }$ 
B)  $\frac { 8 } { 127 }$ 
C)  $- \frac { 16 } { 127 }$ 
D)  $- \frac { 8 } { 127 }$ 
E)  $\frac { 16 } { 127 }$

Question 14

Find the solution set of the system. $\left\{ \begin{array} { l } 
y \leq - 4 \
x > - 4
\end{array} \right.$

Accepted Answer

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

Question 15

A diet requires at least 26 units of vitamin C and at least 31 units of vitamin B complex.Two food supplements are available that provide these nutrients, in the amounts and costs shown in the table
Below.How much of each should be used to minimize the cost?

Accepted Answer

A)  $\quad 7$ grams of $A$ and 5 grams of B: 62 cents 
B)  5 grams of A and 2 grams of B: 32 cents 
C)  5 grams of A and 7 grams of B: 58 cents 
D)  $\quad 3$ grams of $A$ and 9 grams of B: 54 cents 
E)  1 gram of $A$ and 5 grams of $B : 34$ cents 
A)  $\quad 7$ grams of $A$ and 5 grams of B: 62 cents 
B)  5 grams of A and 2 grams of B: 32 cents 
C)  5 grams of A and 7 grams of B: 58 cents 
D)  $\quad 3$ grams of $A$ and 9 grams of B: 54 cents 
E)  1 gram of $A$ and 5 grams of $B : 34$ cents

Question 16

Find $7 A$.
$$A = \left[ \begin{array} { l l } 
4 & 5 \
4 & 6
\end{array} \right]$$

Accepted Answer

A)  $\left[ \begin{array} { c c } 4 & 35 \ 28 & 42 \end{array} \right]$ 
B)  $\left[ \begin{array} { c c } 28 & 5 \ 4 & 6 \end{array} \right]$ 
C)  $\left[ \begin{array} { c c } 28 & 5 \ 28 & 42 \end{array} \right]$ 
D)  $\left[ \begin{array} { l l } 4 & 35 \ 4 & 42 \end{array} \right]$ 
E)  $\left[ \begin{array} { l l } 28 & 35 \ 28 & 42 \end{array} \right]$ 
A)  $\left[ \begin{array} { c c } 4 & 35 \ 28 & 42 \end{array} \right]$ 
B)  $\left[ \begin{array} { c c } 28 & 5 \ 4 & 6 \end{array} \right]$ 
C)  $\left[ \begin{array} { c c } 28 & 5 \ 28 & 42 \end{array} \right]$ 
D)  $\left[ \begin{array} { l l } 4 & 35 \ 4 & 42 \end{array} \right]$ 
E)  $\left[ \begin{array} { l l } 28 & 35 \ 28 & 42 \end{array} \right]$

Question 17

Find the solution set of the system. $$\left\{ \begin{array} { l } 
y < 7 x + 3 \
y < - 3 x + 7
\end{array} \right.$$

Accepted Answer

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

Question 18

Two artists make winter yard ornaments. They get $\$ 97$ for each wooden snowman they make and $\$ 77$ for each wooden Santa Claus. On average, Nina must work 4 hours and Roberta 3 hours to make a snowman. Nina must work 2 hours and Roberta 4 hours to make a Santa Claus. If neither wishes to work more than 20 hours per week, how many of each ornament should they make each week to maximize their income? The information is summarized in the table below.

Accepted Answer

A)  $\quad 4$ snowmen and 3 ornaments of Santa Claus: $\$ 19$ 
B)  $\quad 3$ snowmen and 4 ornaments of Santa Claus: $\$ 19$ 
C)  $\quad 2$ snowmen and 5 ornaments of Santa Claus: $\$ 23$ 
D)  $\quad 5$ snowmen and no ornaments of Santa Claus: \$485 
E)  4 snowmen and 2 ornaments of Santa Claus: $\$ 542$ 
A)  $\quad 4$ snowmen and 3 ornaments of Santa Claus: $\$ 19$ 
B)  $\quad 3$ snowmen and 4 ornaments of Santa Claus: $\$ 19$ 
C)  $\quad 2$ snowmen and 5 ornaments of Santa Claus: $\$ 23$ 
D)  $\quad 5$ snowmen and no ornaments of Santa Claus: \$485 
E)  4 snowmen and 2 ornaments of Santa Claus: $\$ 542$

Question 19

Solve the system by Gauss-Jordan elimination, if possible. If $( x , y )$ is the solution to the system, give the value of $x$.
$$\left\{ \begin{array} { r } 
x - 2 y = 35 \
y = - 15
\end{array} \right.$$

Accepted Answer

A)  $- 6$ 
B)  5 
C)  6 
D)  $- 5$ 
E)  no solution 
A)  $- 6$ 
B)  5 
C)  6 
D)  $- 5$ 
E)  no solution

Question 20

A diet requires at least 24 units of vitamin C and at least 26 units of vitamin B complex.Two food supplements are available that provide these nutrients, in the amounts and costs shown in the table
Below.How much of each should be used to minimize the cost?

Accepted Answer

A)  $\quad 3$ grams of $A$ and 9 grams of $B : 33$ cents 
B)  1 gram of $A$ and 5 grams of B: 27 cents 
C)  $\quad 5$ grams of $A$ and 7 grams of B: 39 cents 
D)  $\quad 7$ grams of $A$ and 5 grams of B: 45 cents 
E)  5 grams of $A$ and 2 grams of B: 20 cents 
A)  $\quad 3$ grams of $A$ and 9 grams of $B : 33$ cents 
B)  1 gram of $A$ and 5 grams of B: 27 cents 
C)  $\quad 5$ grams of $A$ and 7 grams of B: 39 cents 
D)  $\quad 7$ grams of $A$ and 5 grams of B: 45 cents 
E)  5 grams of $A$ and 2 grams of B: 20 cents

Find the solution set of the system. $\left\{ \begin{array} { l } y < 5 x + 4 \\y < - 4 x + 5\end{array} \right.$

Solve the system using Gaussian elimination. If $( x , y )$ is the solution to the system, give the value of $2 x - y$ . $\left\{ \begin{array} { c } x + y = 24 \\x - 2 y = - 3\end{array} \right.$

Use Cramer's rule to find the solution of the system, if possible. $\left\{ \begin{array} { c } x - y - z = 2 \\x + y + z = 18 \\- x - y + z = - 12\end{array} \right.$

Find values of x and y, if any, that will make the matrices equal. $\left[ \begin{array} { l l } x & y \\1 & 6\end{array} \right] = \left[ \begin{array} { l l } 2 & 9 \\1 & 6\end{array} \right]$

Find the graph of the linear inequality. $3 y \geq 2 x - 9$

Evaluate the determinant. $\left| \begin{array} { c c } 8 & 10 \\ - 8 & 4 \end{array} \right|$

Decompose the fraction into partial fractions. $\frac { 9 x ^ { 2 } + 8 x + 9 } { x ^ { 3 } + x }$

Find the graph of the linear inequality. $2 x - 4 y > 2$

Find the solution set of the system. $\left\{ \begin{array} { l } y \leq - 4 \\x > - 4\end{array} \right.$

Find the inverse of the matrix. $\left[ \begin{array} { c c c } 32 & 1 & - 1 \\32 & 32 & - 1 \\- 1 & - 1 & 1\end{array} \right]$

Solve the system by the addition method, if possible. If a solution exists, give the value of x. $\left\{ \begin{array} { l } 4 ( x + y ) = y + 17 \\7 ( x + 1 ) = y + 18\end{array} \right.$

Illustration shows three circles traced out by a figure skater during her performance.If the centers of the circles are the given distances apart, find the radius of each circle. $A = 10 , B = 18 , C = 20$

What is element $a _ { 11 }$ of the inverse of the following matrix? $\left[ \begin{array} { c c } 16 & 1 \\1 & 8\end{array} \right]$

Find the solution set of the system. $\left\{ \begin{array} { l } y \leq - 4 \\x > - 4\end{array} \right.$

A diet requires at least 26 units of vitamin C and at least 31 units of vitamin B complex.Two food supplements are available that provide these nutrients, in the amounts and costs shown in the table Below.How much of each should be used to minimize the cost?

Find $7 A$ . $A = \left[ \begin{array} { l l } 4 & 5 \\4 & 6\end{array} \right]$

Find the solution set of the system. $\left\{ \begin{array} { l } y < 7 x + 3 \\y < - 3 x + 7\end{array} \right.$

Solve the system by Gauss-Jordan elimination, if possible. If $( x , y )$ is the solution to the system, give the value of $x$ . $\left\{ \begin{array} { r } x - 2 y = 35 \\y = - 15\end{array} \right.$

A diet requires at least 24 units of vitamin C and at least 26 units of vitamin B complex.Two food supplements are available that provide these nutrients, in the amounts and costs shown in the table Below.How much of each should be used to minimize the cost?

A Review of Basic Algebra

Equations and Inequalities

The Rectangular Coordinate System and Graphs of Equations

Functions Functions and Function Notation

Exponential and Logarithmic Functions

Solving Polynomial Equations

Conic Sections and Quadratic Systems

Natural Number Functions and Probability

Filters

Exam 7: Linear Systems

Find the solution set of the system. {y<5x+4y<−4x+5\left\{ \begin{array} { l } y < 5 x + 4 \\y < - 4 x + 5\end{array} \right.{y<5x+4y<−4x+5​

Solve the system using Gaussian elimination. If (x,y)( x , y )(x,y) is the solution to the system, give the value of 2x−y2 x - y2x−y . {x+y=24x−2y=−3\left\{ \begin{array} { c } x + y = 24 \\x - 2 y = - 3\end{array} \right.{x+y=24x−2y=−3​

Use Cramer's rule to find the solution of the system, if possible. {x−y−z=2x+y+z=18−x−y+z=−12\left\{ \begin{array} { c } x - y - z = 2 \\x + y + z = 18 \\- x - y + z = - 12\end{array} \right.⎩⎨⎧​x−y−z=2x+y+z=18−x−y+z=−12​

Find values of x and y, if any, that will make the matrices equal. [xy16]=[2916]\left[ \begin{array} { l l } x & y \\1 & 6\end{array} \right] = \left[ \begin{array} { l l } 2 & 9 \\1 & 6\end{array} \right][x1​y6​]=[21​96​]

Find the graph of the linear inequality. 3y≥2x−93 y \geq 2 x - 93y≥2x−9

Evaluate the determinant. ∣810−84∣\left| \begin{array} { c c } 8 & 10 \\ - 8 & 4 \end{array} \right|​8−8​104​​

Decompose the fraction into partial fractions. 9x2+8x+9x3+x\frac { 9 x ^ { 2 } + 8 x + 9 } { x ^ { 3 } + x }x3+x9x2+8x+9​

Find the graph of the linear inequality. 2x−4y>22 x - 4 y > 22x−4y>2

Find the solution set of the system. {y≤−4x>−4\left\{ \begin{array} { l } y \leq - 4 \\x > - 4\end{array} \right.{y≤−4x>−4​

Find the inverse of the matrix. [321−13232−1−1−11]\left[ \begin{array} { c c c } 32 & 1 & - 1 \\32 & 32 & - 1 \\- 1 & - 1 & 1\end{array} \right]​3232−1​132−1​−1−11​​

Solve the system by the addition method, if possible. If a solution exists, give the value of x. {4(x+y)=y+177(x+1)=y+18\left\{ \begin{array} { l } 4 ( x + y ) = y + 17 \\7 ( x + 1 ) = y + 18\end{array} \right.{4(x+y)=y+177(x+1)=y+18​

Illustration shows three circles traced out by a figure skater during her performance.If the centers of the circles are the given distances apart, find the radius of each circle. A=10,B=18,C=20A = 10 , B = 18 , C = 20A=10,B=18,C=20

What is element a11a _ { 11 }a11​ of the inverse of the following matrix? [16118]\left[ \begin{array} { c c } 16 & 1 \\1 & 8\end{array} \right][161​18​]

Find the solution set of the system. {y≤−4x>−4\left\{ \begin{array} { l } y \leq - 4 \\x > - 4\end{array} \right.{y≤−4x>−4​

A diet requires at least 26 units of vitamin C and at least 31 units of vitamin B complex.Two food supplements are available that provide these nutrients, in the amounts and costs shown in the table Below.How much of each should be used to minimize the cost?

Find 7A7 A7A . A=[4546]A = \left[ \begin{array} { l l } 4 & 5 \\4 & 6\end{array} \right]A=[44​56​]

Find the solution set of the system. {y<7x+3y<−3x+7\left\{ \begin{array} { l } y < 7 x + 3 \\y < - 3 x + 7\end{array} \right.{y<7x+3y<−3x+7​

Solve the system by Gauss-Jordan elimination, if possible. If (x,y)( x , y )(x,y) is the solution to the system, give the value of xxx . {x−2y=35y=−15\left\{ \begin{array} { r } x - 2 y = 35 \\y = - 15\end{array} \right.{x−2y=35y=−15​

A diet requires at least 24 units of vitamin C and at least 26 units of vitamin B complex.Two food supplements are available that provide these nutrients, in the amounts and costs shown in the table Below.How much of each should be used to minimize the cost?

A Review of Basic Algebra

Equations and Inequalities

The Rectangular Coordinate System and Graphs of Equations

Functions Functions and Function Notation

Exponential and Logarithmic Functions

Solving Polynomial Equations

Conic Sections and Quadratic Systems

Natural Number Functions and Probability

Filters

Find the solution set of the system. $\left\{ \begin{array} { l } y < 5 x + 4 \\y < - 4 x + 5\end{array} \right.$

Solve the system using Gaussian elimination. If $( x , y )$ is the solution to the system, give the value of $2 x - y$ . $\left\{ \begin{array} { c } x + y = 24 \\x - 2 y = - 3\end{array} \right.$

Use Cramer's rule to find the solution of the system, if possible. $\left\{ \begin{array} { c } x - y - z = 2 \\x + y + z = 18 \\- x - y + z = - 12\end{array} \right.$

Find values of x and y, if any, that will make the matrices equal. $\left[ \begin{array} { l l } x & y \\1 & 6\end{array} \right] = \left[ \begin{array} { l l } 2 & 9 \\1 & 6\end{array} \right]$

Find the graph of the linear inequality. $3 y \geq 2 x - 9$

Evaluate the determinant. $\left| \begin{array} { c c } 8 & 10 \\ - 8 & 4 \end{array} \right|$

Decompose the fraction into partial fractions. $\frac { 9 x ^ { 2 } + 8 x + 9 } { x ^ { 3 } + x }$

Find the graph of the linear inequality. $2 x - 4 y > 2$

Find the solution set of the system. $\left\{ \begin{array} { l } y \leq - 4 \\x > - 4\end{array} \right.$

Find the inverse of the matrix. $\left[ \begin{array} { c c c } 32 & 1 & - 1 \\32 & 32 & - 1 \\- 1 & - 1 & 1\end{array} \right]$

Solve the system by the addition method, if possible. If a solution exists, give the value of x. $\left\{ \begin{array} { l } 4 ( x + y ) = y + 17 \\7 ( x + 1 ) = y + 18\end{array} \right.$

Illustration shows three circles traced out by a figure skater during her performance.If the centers of the circles are the given distances apart, find the radius of each circle. $A = 10 , B = 18 , C = 20$

What is element $a _ { 11 }$ of the inverse of the following matrix? $\left[ \begin{array} { c c } 16 & 1 \\1 & 8\end{array} \right]$

Find the solution set of the system. $\left\{ \begin{array} { l } y \leq - 4 \\x > - 4\end{array} \right.$

Find $7 A$ . $A = \left[ \begin{array} { l l } 4 & 5 \\4 & 6\end{array} \right]$

Find the solution set of the system. $\left\{ \begin{array} { l } y < 7 x + 3 \\y < - 3 x + 7\end{array} \right.$

Solve the system by Gauss-Jordan elimination, if possible. If $( x , y )$ is the solution to the system, give the value of $x$ . $\left\{ \begin{array} { r } x - 2 y = 35 \\y = - 15\end{array} \right.$