Question 1

Determine if the given ordered triple is a solution of the system.
-$$\begin{array} { l } 
( - 3,1,3 ) \
x + y + z = 1 \
x - y + 2 z = - 4 \
4 x + y + z = 10
\end{array}$$

Accepted Answer

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

Question 2

Determine the real solutions to the system of nonlinear equations.
-$$\begin{array} { l } 
x ^ { 3 } + y = 0 \
6 x ^ { 2 } - y = 0
\end{array}$$

Accepted Answer

A)  $( 0,0 ) , ( - 6,36 )$ 
B)  $( - 1,1 ) , ( - 6,216 )$ 
C)  $( 0,0 ) , ( 6 , - 216 )$ 
D)  $( 0,0 ) , ( - 6,216 )$ 
A)  $( 0,0 ) , ( - 6,36 )$ 
B)  $( - 1,1 ) , ( - 6,216 )$ 
C)  $( 0,0 ) , ( 6 , - 216 )$ 
D)  $( 0,0 ) , ( - 6,216 )$

Question 3

Graph the inequality.
-$$y \leq x ^ { 2 } + 1$$

Accepted Answer

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

Question 4

Graph the system of inequalities.
-$$\begin{array} { l } 
x + y \leq 9 \
x + y \geq 1 \
y \geq 0 \
x \geq 0
\end{array}$$

Accepted Answer

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

Question 5

Graph the inequality.
-$$y < - \frac { 4 } { 3 } x$$

Accepted Answer

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

Question 6

Determine the real solutions to the system of nonlinear equations.
-$x y = 1$
$7 x - y = - 6$

Accepted Answer

A)  $( - 7,7 ) , ( 1 , - 1 )$ 
B)  $\left( 7 , \frac { 1 } { 7 } \right) , ( - 1 , - 1 )$ 
C)  $( - 1 , - 1 )$ 
D)  $\left( \frac { 1 } { 7 } , 7 \right) , ( - 1 , - 1 )$ 
A)  $( - 7,7 ) , ( 1 , - 1 )$ 
B)  $\left( 7 , \frac { 1 } { 7 } \right) , ( - 1 , - 1 )$ 
C)  $( - 1 , - 1 )$ 
D)  $\left( \frac { 1 } { 7 } , 7 \right) , ( - 1 , - 1 )$

Question 7

Graph the system of inequalities.
-$\begin{array}{l}
4 x+y \geq 4 \
4 x+y \geq 0
\end{array}$

Accepted Answer

A) 
  
B) 
  
C)  No solution
  
D) 
  
A) 
  
B) 
  
C)  No solution
  
D)

Question 8

Determine the real solutions to the system of nonlinear equations.
-$$\begin{array} { l } 
x ^ { 2 } + y ^ { 2 } = 4 \
x ^ { 2 } - y ^ { 2 } = 4
\end{array}$$

Accepted Answer

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

Question 9

Write the partial fraction decomposition of the rational expression.
-$\frac { 80 - 14 x } { x ( x - 4 ) ^ { 2 } }$

Accepted Answer

A)  $\frac { 5 } { x } + \frac { - 5 } { x - 4 } + \frac { 6 } { ( x - 4 ) ^ { 2 } }$ 
B)  $\frac { 5 } { x } + \frac { - 5 } { x - 4 } + \frac { 12 } { ( x - 4 ) ^ { 2 } }$ 
C)  $\frac { 5 } { x } + \frac { 6 } { x - 4 } + \frac { - 5 } { ( x - 4 ) ^ { 2 } }$ 
D)  $\frac { - 5 } { x } + \frac { 5 } { x - 4 } + \frac { 6 } { ( x - 4 ) ^ { 2 } }$ 
A)  $\frac { 5 } { x } + \frac { - 5 } { x - 4 } + \frac { 6 } { ( x - 4 ) ^ { 2 } }$ 
B)  $\frac { 5 } { x } + \frac { - 5 } { x - 4 } + \frac { 12 } { ( x - 4 ) ^ { 2 } }$ 
C)  $\frac { 5 } { x } + \frac { 6 } { x - 4 } + \frac { - 5 } { ( x - 4 ) ^ { 2 } }$ 
D)  $\frac { - 5 } { x } + \frac { 5 } { x - 4 } + \frac { 6 } { ( x - 4 ) ^ { 2 } }$

Question 10

Solve the system of linear equations using the elimination method.
-$$\begin{aligned}
- 3 x - y - 6 z = & - 75 \
5 x + 5 y - 5 z = & 35 \
- 9 x - 7 y + z = & - 109
\end{aligned}$$

Accepted Answer

A) (-6, 9, 12) 
B) (6, 9, 8) 
C) (12, 9, -6) 
D) (6, 8, 9) 
A) (-6, 9, 12) 
B) (6, 9, 8) 
C) (12, 9, -6) 
D) (6, 8, 9)

Question 11

Determine the real solutions to the system of nonlinear equations.
-$$\begin{array} { l } 
x ^ { 2 } + y ^ { 2 } = 25 \
x + y = 7
\end{array}$$

Accepted Answer

A) (4, -3), (3, -4) 
B) (4, 3), (3, 4) 
C) (-4, 3), (-3, 4) 
D) (-4, -3), (-3, -4) 
A) (4, -3), (3, -4) 
B) (4, 3), (3, 4) 
C) (-4, 3), (-3, 4) 
D) (-4, -3), (-3, -4)

Question 12

Solve the problem.
-The Family Fine Arts Center charges $20 per adult and $11 per senior citizen for its performances. On a recent weekend evening when 514 people paid admission, the total receipts were $7175. How many who paid were senior citizens?

Accepted Answer

A) 259 senior citizens 
B) 255 senior citizens 
C) 169 senior citizens 
D) 345 senior citizens 
A) 259 senior citizens 
B) 255 senior citizens 
C) 169 senior citizens 
D) 345 senior citizens

Question 13

Determine if the ordered pair is a solution to the given inequality.
-$$3 x ^ { 2 } - y \leq 9 ; ( - 0.5,5.5 )$$

Accepted Answer

A) Yes 
B) No 
A) Yes 
B) No

Question 14

Use the substitution method or the elimination method to solve the system. If the system has infinitely many solutions, express the ordered pair in terms of x or y.
-6x - 5y = 1 
30x - 25y = 4

Accepted Answer

A) (1, 4) 
B) (5, 4) 
C) 
$\left( \frac { 5 } { 36 } , \frac { 1 } { 6 } \right)$ 
D) no solution 
A) (1, 4) 
B) (5, 4) 
C) 
$\left( \frac { 5 } { 36 } , \frac { 1 } { 6 } \right)$ 
D) no solution

Question 15

Use Gauss-Jordan elimination to solve the linear system and determine whether the system has a unique solution, no solution, or infinitely many solutions. If the system has infinitely many solutions, describe the solution as an ordered
triple involving variable z.
-$$\begin{array} { r r } 
x + y + z & = 9 \
2 x - 3 y + 4 z & = 7 \
x - 4 y + 3 z & = - 2
\end{array}$$

Accepted Answer

A)  $\left( - \frac { 7 z } { 5 } + \frac { 34 } { 5 } , \frac { 2 z } { 5 } + \frac { 11 } { 5 } , z \right)$ 
B)  $\left( \frac { 7 z } { 5 } + \frac { 34 } { 5 } , \frac { 2 z } { 5 } - \frac { 11 } { 5 } , z \right)$ 
C)  $\left( - \frac { 7 z } { 5 } + \frac { 34 } { 5 } , \frac { 2 z } { 5 } - \frac { 11 } { 5 } , z \right)$ 
D)  $\left( \frac { z } { 5 } + \frac { 34 } { 5 } , \frac { 2 z } { 5 } + \frac { 11 } { 5 } , z \right)$ 
A)  $\left( - \frac { 7 z } { 5 } + \frac { 34 } { 5 } , \frac { 2 z } { 5 } + \frac { 11 } { 5 } , z \right)$ 
B)  $\left( \frac { 7 z } { 5 } + \frac { 34 } { 5 } , \frac { 2 z } { 5 } - \frac { 11 } { 5 } , z \right)$ 
C)  $\left( - \frac { 7 z } { 5 } + \frac { 34 } { 5 } , \frac { 2 z } { 5 } - \frac { 11 } { 5 } , z \right)$ 
D)  $\left( \frac { z } { 5 } + \frac { 34 } { 5 } , \frac { 2 z } { 5 } + \frac { 11 } { 5 } , z \right)$

Question 16

Determine the real solutions to the system of nonlinear equations.
-$$\begin{array} { l } 
x y = 0 \
x + y = - 9
\end{array}$$

Accepted Answer

A)  $( - 9,0 ) , ( 0 , - 9 )$ 
B)  $( 9,0 ) , ( 0,9 )$ 
C)  $( 9,0 ) , ( 0 , - 9 )$ 
D)  $( - 9,0 ) , ( 0,9 )$ 
A)  $( - 9,0 ) , ( 0 , - 9 )$ 
B)  $( 9,0 ) , ( 0,9 )$ 
C)  $( 9,0 ) , ( 0 , - 9 )$ 
D)  $( - 9,0 ) , ( 0,9 )$

Question 17

Write the partial fraction decomposition of the rational expression.
-$\frac { 11 x + 1 } { x ^ { 3 } - 1 }$

Accepted Answer

A)  $\frac { 4 } { x - 1 } + \frac { 3 x - 4 } { x ^ { 2 } + x + 1 }$ 
B)  $\frac { - 4 } { x - 1 } + \frac { 4 x + 3 } { x ^ { 2 } + x + 1 }$ 
C)  $\frac { 4 } { x - 1 } + \frac { - 4 } { x + 1 } + \frac { 3 } { x - 1 }$ 
D)  $\frac { 4 } { x - 1 } + \frac { - 4 x + 3 } { x ^ { 2 } + x + 1 }$ 
A)  $\frac { 4 } { x - 1 } + \frac { 3 x - 4 } { x ^ { 2 } + x + 1 }$ 
B)  $\frac { - 4 } { x - 1 } + \frac { 4 x + 3 } { x ^ { 2 } + x + 1 }$ 
C)  $\frac { 4 } { x - 1 } + \frac { - 4 } { x + 1 } + \frac { 3 } { x - 1 }$ 
D)  $\frac { 4 } { x - 1 } + \frac { - 4 x + 3 } { x ^ { 2 } + x + 1 }$

Question 18

Determine the real solutions to the system of nonlinear equations.
-$$\begin{array} { l } 
x ^ { 2 } + y ^ { 2 } = 16 \
16 x ^ { 2 } + 25 y ^ { 2 } = 400
\end{array}$$

Accepted Answer

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

Question 19

Use Gauss-Jordan elimination to solve the linear system and determine whether the system has a unique solution, no solution, or infinitely many solutions. If the system has infinitely many solutions, describe the solution as an ordered
triple involving variable z.
-$$\begin{array} { l } 
5 x - y + z = 8 \
7 x + y + z = 6
\end{array}$$

Accepted Answer

A)  no solution 
B)  $( - z + 3,4 z + 7 , z )$ 
C)  $\left( \frac { 1 } { 6 } z + \frac { 7 } { 6 } , \frac { 1 } { 6 } z , z \right)$ 
D)  $\left( - \frac { 1 } { 6 } z + \frac { 7 } { 6 } , \frac { 1 } { 6 } z - \frac { 13 } { 6 } , z \right)$ 
A)  no solution 
B)  $( - z + 3,4 z + 7 , z )$ 
C)  $\left( \frac { 1 } { 6 } z + \frac { 7 } { 6 } , \frac { 1 } { 6 } z , z \right)$ 
D)  $\left( - \frac { 1 } { 6 } z + \frac { 7 } { 6 } , \frac { 1 } { 6 } z - \frac { 13 } { 6 } , z \right)$

Question 20

Graph the system of inequalities.
-$\begin{array}{l}
2 x+3 y \leq 6 \
x-y \leq 3
\end{array}$

Accepted Answer

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

Determine if the given ordered triple is a solution of the system. - (-3,1,3) x+y+z=1 x-y+2z=-4 4x+y+z=10

Determine the real solutions to the system of nonlinear equations. - +y=0 6-y=0

Graph the inequality. - $y \leq x ^ { 2 } + 1$ $Graph the inequality. - y \leq x ^ { 2 } + 1$

Graph the system of inequalities. - x+y\leq9 x+y\geq1 y\geq0 x\geq0 $Graph the system of inequalities. - \begin{array} { l } x + y \leq 9 \\ x + y \geq 1 \\ y \geq 0 \\ x \geq 0 \end{array}$

Graph the inequality. - $y < - \frac { 4 } { 3 } x$ $Graph the inequality. - y < - \frac { 4 } { 3 } x$

Determine the real solutions to the system of nonlinear equations. - $x y = 1$ $7 x - y = - 6$

Graph the system of inequalities. - 4x+y\geq4 4x+y\geq0 $Graph the system of inequalities. - \begin{array}{l} 4 x+y \geq 4 \\ 4 x+y \geq 0 \end{array}$

Determine the real solutions to the system of nonlinear equations. - +=4 -=4

Write the partial fraction decomposition of the rational expression. - $\frac { 80 - 14 x } { x ( x - 4 ) ^ { 2 } }$

Solve the system of linear equations using the elimination method. - -3x-y-6z= -75 5x+5y-5z= 35 -9x-7y+z= -109

Determine the real solutions to the system of nonlinear equations. - +=25 x+y=7

Solve the problem. -The Family Fine Arts Center charges $20 per adult and $11 per senior citizen for its performances. On a recent weekend evening when 514 people paid admission, the total receipts were $7175. How many who paid were senior citizens?

Determine if the ordered pair is a solution to the given inequality. - $3 x ^ { 2 } - y \leq 9 ; ( - 0.5,5.5 )$

Use the substitution method or the elimination method to solve the system. If the system has infinitely many solutions, express the ordered pair in terms of x or y. -6x - 5y = 1 30x - 25y = 4

Use Gauss-Jordan elimination to solve the linear system and determine whether the system has a unique solution, no solution, or infinitely many solutions. If the system has infinitely many solutions, describe the solution as an ordered triple involving variable z. - x+y+z =9 2x-3y+4z =7 x-4y+3z =-2

Determine the real solutions to the system of nonlinear equations. - xy=0 x+y=-9

Write the partial fraction decomposition of the rational expression. - $\frac { 11 x + 1 } { x ^ { 3 } - 1 }$

Determine the real solutions to the system of nonlinear equations. - +=16 16+25=400

Use Gauss-Jordan elimination to solve the linear system and determine whether the system has a unique solution, no solution, or infinitely many solutions. If the system has infinitely many solutions, describe the solution as an ordered triple involving variable z. - 5x-y+z=8 7x+y+z=6

Graph the system of inequalities. - 2x+3y\leq6 x-y\leq3 $Graph the system of inequalities. - \begin{array}{l} 2 x+3 y \leq 6 \\ x-y \leq 3 \end{array}$

Equations, Inequalities, and Applications

The Rectangular Coordinate System, Lines, and Circles

Functions

Polynomial and Rational Functions

Exponential and Logarithmic Functions and Equations

Conic Sections

Matrices

Sequences and Series; Counting and Probability

Math Exercises: Sets, Intervals, Absolute Value, and Properties

Filters

Exam 7: Systems of Equations and Inequalities

Determine if the given ordered triple is a solution of the system. - (-3,1,3) x+y+z=1 x-y+2z=-4 4x+y+z=10

Determine the real solutions to the system of nonlinear equations. - +y=0 6-y=0

Graph the inequality. - y≤x2+1y \leq x ^ { 2 } + 1y≤x2+1

Graph the system of inequalities. - x+y\leq9 x+y\geq1 y\geq0 x\geq0

Graph the inequality. - y<−43xy < - \frac { 4 } { 3 } xy<−34​x

Determine the real solutions to the system of nonlinear equations. - xy=1x y = 1xy=1 7x−y=−67 x - y = - 67x−y=−6

Graph the system of inequalities. - 4x+y\geq4 4x+y\geq0

Determine the real solutions to the system of nonlinear equations. - +=4 -=4

Write the partial fraction decomposition of the rational expression. - 80−14xx(x−4)2\frac { 80 - 14 x } { x ( x - 4 ) ^ { 2 } }x(x−4)280−14x​

Solve the system of linear equations using the elimination method. - -3x-y-6z= -75 5x+5y-5z= 35 -9x-7y+z= -109

Determine the real solutions to the system of nonlinear equations. - +=25 x+y=7

Solve the problem. -The Family Fine Arts Center charges $20 per adult and $11 per senior citizen for its performances. On a recent weekend evening when 514 people paid admission, the total receipts were $7175. How many who paid were senior citizens?

Determine if the ordered pair is a solution to the given inequality. - 3x2−y≤9;(−0.5,5.5)3 x ^ { 2 } - y \leq 9 ; ( - 0.5,5.5 )3x2−y≤9;(−0.5,5.5)

Use the substitution method or the elimination method to solve the system. If the system has infinitely many solutions, express the ordered pair in terms of x or y. -6x - 5y = 1 30x - 25y = 4

Use Gauss-Jordan elimination to solve the linear system and determine whether the system has a unique solution, no solution, or infinitely many solutions. If the system has infinitely many solutions, describe the solution as an ordered triple involving variable z. - x+y+z =9 2x-3y+4z =7 x-4y+3z =-2

Determine the real solutions to the system of nonlinear equations. - xy=0 x+y=-9

Write the partial fraction decomposition of the rational expression. - 11x+1x3−1\frac { 11 x + 1 } { x ^ { 3 } - 1 }x3−111x+1​

Determine the real solutions to the system of nonlinear equations. - +=16 16+25=400

Use Gauss-Jordan elimination to solve the linear system and determine whether the system has a unique solution, no solution, or infinitely many solutions. If the system has infinitely many solutions, describe the solution as an ordered triple involving variable z. - 5x-y+z=8 7x+y+z=6

Graph the system of inequalities. - 2x+3y\leq6 x-y\leq3

Equations, Inequalities, and Applications

The Rectangular Coordinate System, Lines, and Circles

Functions

Polynomial and Rational Functions

Exponential and Logarithmic Functions and Equations

Conic Sections

Matrices

Sequences and Series; Counting and Probability

Math Exercises: Sets, Intervals, Absolute Value, and Properties

Filters

Graph the inequality. - $y \leq x ^ { 2 } + 1$ $Graph the inequality. - y \leq x ^ { 2 } + 1$

Graph the system of inequalities. - x+y\leq9 x+y\geq1 y\geq0 x\geq0 $Graph the system of inequalities. - \begin{array} { l } x + y \leq 9 \\ x + y \geq 1 \\ y \geq 0 \\ x \geq 0 \end{array}$

Graph the inequality. - $y < - \frac { 4 } { 3 } x$ $Graph the inequality. - y < - \frac { 4 } { 3 } x$

Determine the real solutions to the system of nonlinear equations. - $x y = 1$ $7 x - y = - 6$

Graph the system of inequalities. - 4x+y\geq4 4x+y\geq0 $Graph the system of inequalities. - \begin{array}{l} 4 x+y \geq 4 \\ 4 x+y \geq 0 \end{array}$

Write the partial fraction decomposition of the rational expression. - $\frac { 80 - 14 x } { x ( x - 4 ) ^ { 2 } }$

Determine if the ordered pair is a solution to the given inequality. - $3 x ^ { 2 } - y \leq 9 ; ( - 0.5,5.5 )$

Write the partial fraction decomposition of the rational expression. - $\frac { 11 x + 1 } { x ^ { 3 } - 1 }$

Graph the system of inequalities. - 2x+3y\leq6 x-y\leq3 $Graph the system of inequalities. - \begin{array}{l} 2 x+3 y \leq 6 \\ x-y \leq 3 \end{array}$