Question 1

Determine the real solutions to the system of nonlinear equations.
-$$\begin{array} { l } 
y = x - 3 \
y ^ { 2 } = - 12 x
\end{array}$$

Accepted Answer

A)  $( - 3 , - 6 ) , ( - 3,6 ) , ( 3,0 )$ 
B)  $( - 3 , - 6 ) , ( 3,0 )$ 
C)  $( - 3 , - 6 )$ 
D)  $( - 3 , - 6 ) , ( - 3,6 )$ 
A)  $( - 3 , - 6 ) , ( - 3,6 ) , ( 3,0 )$ 
B)  $( - 3 , - 6 ) , ( 3,0 )$ 
C)  $( - 3 , - 6 )$ 
D)  $( - 3 , - 6 ) , ( - 3,6 )$ C

Question 2

Solve the system of linear equations. If the system has infinitely many solutions, describe the solution with an ordered triple in terms of variable z.
-$$\begin{aligned}
x + 3 y + 2 z & = 11 \
4 y + 9 z & = - 12 \
x + 7 y + 11 z & = - 1
\end{aligned}$$

Accepted Answer

A)  $\left( \frac { 19 z } { 4 } + 20 , - \frac { 9 z } { 4 } + 3 , z \right)$ 
B)  $\left( - \frac { 19 z } { 4 } + 20 , - \frac { 9 z } { 4 } + 3 , z \right)$ 
C)  $\left( \frac { 19 \mathrm { z } } { 4 } + 20 , - \frac { 9 \mathrm { z } } { 4 } - 3 , \mathrm { z } \right\}$ 
D)  $\left( \frac { 19 z } { 4 } + 20 , \frac { 9 z } { 4 } + 3 , z \right)$ 
A)  $\left( \frac { 19 z } { 4 } + 20 , - \frac { 9 z } { 4 } + 3 , z \right)$ 
B)  $\left( - \frac { 19 z } { 4 } + 20 , - \frac { 9 z } { 4 } + 3 , z \right)$ 
C)  $\left( \frac { 19 \mathrm { z } } { 4 } + 20 , - \frac { 9 \mathrm { z } } { 4 } - 3 , \mathrm { z } \right\}$ 
D)  $\left( \frac { 19 z } { 4 } + 20 , \frac { 9 z } { 4 } + 3 , z \right)$ C

Question 3

Determine if each ordered pair is a solution to the given system of inequalities in two variables.
-$$\begin{array} { l } 
x ^ { 2 } + y ^ { 2 } = 61 \
x + y = - 11
\end{array}$$
(i) $( 5,6 )$; (ii) $( 6,5 )$

Accepted Answer

A)  (i) No; (ii) Yes 
B)  (i) Yes; (ii) Yes 
C)  (i) No; (ii) No 
D)  (i) Yes; (ii) No 
A)  (i) No; (ii) Yes 
B)  (i) Yes; (ii) Yes 
C)  (i) No; (ii) No 
D)  (i) Yes; (ii) No C

Question 4

Graph the inequality.
-$$\frac { x } { 4 } + \frac { y } { 3 } \leq 1$$

Accepted Answer

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

Question 5

Use Gaussian elimination and matrices to solve the system of linear equations. Write your final augmented matrix in triangular form and then solve for each variable using back substitution.
-7x - y + 2z = 63 8x + 2z = 74 4y + z = 25

Accepted Answer

A) (7, 4, 9) 
B) (-7, 4, 14) 
C) (7, 9, 4) 
D) (-7, 14, 4) 
A) (7, 4, 9) 
B) (-7, 4, 14) 
C) (7, 9, 4) 
D) (-7, 14, 4)

Question 6

Determine whether the system corresponding to the given augmented matrix is dependent or inconsistent. If it is
dependent, give the solution.
-$$\left[ \begin{array} { r r r | r } 
1 & 0 & 0 & 0 \
0 & 1 & 0 & 0 \
0 & 0 & 0 & - 4
\end{array} \right]$$

Accepted Answer

A) inconsistent 
B) dependent; z = -4 
C) dependent; (0, -4) 
D) dependent; (0, 0) 
A) inconsistent 
B) dependent; z = -4 
C) dependent; (0, -4) 
D) dependent; (0, 0)

Question 7

Determine the real solutions to the system of nonlinear equations.
-$$\begin{array} { l } 
x ^ { 2 } + y ^ { 2 } = 29 \
- 4 x + y ^ { 2 } = 17
\end{array}$$

Accepted Answer

A)  $( 2,5 )$ 
B)  $( 2,5 ) , ( 2 , - 5 )$ 
C)  $( 2,5 ) , ( 2 , - 5 ) , ( - 6,5 ) , ( - 6 , - 5 )$ 
D)  $( 2,5 ) , ( 2 , - 5 ) , ( - 2,5 ) , ( - 2 , - 5 )$ 
A)  $( 2,5 )$ 
B)  $( 2,5 ) , ( 2 , - 5 )$ 
C)  $( 2,5 ) , ( 2 , - 5 ) , ( - 6,5 ) , ( - 6 , - 5 )$ 
D)  $( 2,5 ) , ( 2 , - 5 ) , ( - 2,5 ) , ( - 2 , - 5 )$

Question 8

Determine the real solutions to the system of nonlinear equations.
-$$\begin{array} { l } 
y = x ^ { 2 } - 2 x + 1 \
y = - x ^ { 2 } + 8 x - 7
\end{array}$$

Accepted Answer

A)  $( 4,9 ) , ( 1,0 )$ 
B)  $( - 4,25 ) , ( 0,1 )$ 
C)  $( - 4,25 ) , ( - 1,4 )$ 
D)  $( 4,9 ) , ( 0,1 )$ 
A)  $( 4,9 ) , ( 1,0 )$ 
B)  $( - 4,25 ) , ( 0,1 )$ 
C)  $( - 4,25 ) , ( - 1,4 )$ 
D)  $( 4,9 ) , ( 0,1 )$

Question 9

Write the partial fraction decomposition of the rational expression.
-$$\frac { 7 x ^ { 2 } - 7 x + 3 } { ( x - 1 ) ^ { 3 } }$$

Accepted Answer

A)  $\frac { 7 } { x - 1 } - \frac { 7 } { ( x - 1 ) ^ { 2 } } + \frac { 3 } { ( x - 1 ) ^ { 3 } }$ 
B)  $\frac { 7 } { x - 1 } + \frac { x + 7 } { ( x - 1 ) ^ { 2 } } + \frac { x ^ { 2 } + 3 } { ( x - 1 ) ^ { 3 } }$ 
C)  $\frac { 7 } { x - 1 } + \frac { 7 } { ( x - 1 ) ^ { 2 } }$ 
D)  $\frac { 7 } { x - 1 } + \frac { 7 } { ( x - 1 ) ^ { 2 } } + \frac { 3 } { ( x - 1 ) ^ { 3 } }$ 
A)  $\frac { 7 } { x - 1 } - \frac { 7 } { ( x - 1 ) ^ { 2 } } + \frac { 3 } { ( x - 1 ) ^ { 3 } }$ 
B)  $\frac { 7 } { x - 1 } + \frac { x + 7 } { ( x - 1 ) ^ { 2 } } + \frac { x ^ { 2 } + 3 } { ( x - 1 ) ^ { 3 } }$ 
C)  $\frac { 7 } { x - 1 } + \frac { 7 } { ( x - 1 ) ^ { 2 } }$ 
D)  $\frac { 7 } { x - 1 } + \frac { 7 } { ( x - 1 ) ^ { 2 } } + \frac { 3 } { ( x - 1 ) ^ { 3 } }$

Question 10

Determine the real solutions to the system of nonlinear equations.
-$$\begin{array} { l } 
x ^ { 2 } + y ^ { 2 } = 169 \
x + y = 17
\end{array}$$

Accepted Answer

A)  $( - 12,5 ) , ( - 5,12 )$ 
B)  $( 12 , - 5 ) , ( 5 , - 12 )$ 
C)  $( - 12 , - 5 ) , ( - 5 , - 12 )$ 
D)  $( 12,5 ) , ( 5,12 )$ 
A)  $( - 12,5 ) , ( - 5,12 )$ 
B)  $( 12 , - 5 ) , ( 5 , - 12 )$ 
C)  $( - 12 , - 5 ) , ( - 5 , - 12 )$ 
D)  $( 12,5 ) , ( 5,12 )$

Question 11

Determine the real solutions to the system of nonlinear equations.
-$$\begin{array} { l } 
y = x ^ { 2 } + 4 \
y = - x ^ { 2 } + 12
\end{array}$$

Accepted Answer

A)  $( 2,8 ) , ( - 2,8 )$ 
B)  $( 8,2 ) , ( 8 , - 2 )$ 
C)  $( 2,8 ) , ( 2 , - 8 ) , ( - 2,8 ) , ( - 2 , - 8 )$ 
D)  $( 2,8 ) , ( 2 , - 8 )$ 
A)  $( 2,8 ) , ( - 2,8 )$ 
B)  $( 8,2 ) , ( 8 , - 2 )$ 
C)  $( 2,8 ) , ( 2 , - 8 ) , ( - 2,8 ) , ( - 2 , - 8 )$ 
D)  $( 2,8 ) , ( 2 , - 8 )$

Question 12

Graph the inequality.
-$$- 2 x - 5 y \leq - 10$$

Accepted Answer

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

Question 13

Determine the real solutions to the system of nonlinear equations.
-$$- 8 x - y = 9$$
$$y = x ^ { 2 } - 2$$

Accepted Answer

A)  $( - 1,3 ) , ( - 7,51 )$ 
B)  $( 1 , - 1 ) , ( - 7,47 )$ 
C)  $( - 1 , - 1 ) , ( - 7,47 )$ 
D)  $( 1 , - 1 ) , ( 7,47 )$ 
A)  $( - 1,3 ) , ( - 7,51 )$ 
B)  $( 1 , - 1 ) , ( - 7,47 )$ 
C)  $( - 1 , - 1 ) , ( - 7,47 )$ 
D)  $( 1 , - 1 ) , ( 7,47 )$

Question 14

Graph the system of inequalities.
-$$\begin{array} { l } 
4 x + 3 y \geq 12 \
x \geq y
\end{array}$$

Accepted Answer

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

Question 15

Solve the problem.
-Find the dimensions of a rectangle whose perimeter is 48 feet and whose area is 135 square feet.

Accepted Answer

A) 10 feet by 14 feet 
B) 9 feet by 15 feet 
C) 8 feet by 14 feet 
D) 8 feet by 16 feet 
A) 10 feet by 14 feet 
B) 9 feet by 15 feet 
C) 8 feet by 14 feet 
D) 8 feet by 16 feet

Question 16

Graph the system of inequalities.
-$\begin{array}{c}
2 x+3 y \geq 6 \
x-y \leq 3 \
x \geq 1
\end{array}$

Accepted Answer

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

Question 17

Solve the system of equations by elimination.
-$\frac { 3 } { 5 } x + \frac { 2 } { 5 } y = \frac { 38 } { 5 }$
6x + 2y = 86

Accepted Answer

A) (-16, 6) 
B) (16, -5) 
C) (-16, 4) 
D) (-5, 16) 
A) (-16, 6) 
B) (16, -5) 
C) (-16, 4) 
D) (-5, 16)

Question 18

Determine if the ordered pair is a solution to the system of linear inequalities in two variables.
-$$\begin{array} { l } 
x + y \geq 2 \
- 3 x + y \leq 11 \
x \geq 0 \
y \geq 1
\end{array}$$

Accepted Answer

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

Question 19

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.
-x + 6y = -3 2x + 12y = -6

Accepted Answer

A) no solution 
B) 
$\left( x , - \frac { 1 } { 6 } x - \frac { 1 } { 2 } \right)$ or $( - 6 y - 3 , y )$ 
C) (0, 0) 
D) (-3, 0) 
A) no solution 
B) 
$\left( x , - \frac { 1 } { 6 } x - \frac { 1 } { 2 } \right)$ or $( - 6 y - 3 , y )$ 
C) (0, 0) 
D) (-3, 0)

Question 20

Graph the inequality.
-

Accepted Answer

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

Determine the real solutions to the system of nonlinear equations. - y=x-3 =-12x

Solve the system of linear equations. If the system has infinitely many solutions, describe the solution with an ordered triple in terms of variable z. - x+3y+2z =11 4y+9z =-12 x+7y+11z =-1

Determine if each ordered pair is a solution to the given system of inequalities in two variables. - +=61 x+y=-11 (i) $( 5,6 )$ ; (ii) $( 6,5 )$

Graph the inequality. - $\frac { x } { 4 } + \frac { y } { 3 } \leq 1$ $Graph the inequality. - \frac { x } { 4 } + \frac { y } { 3 } \leq 1$

Use Gaussian elimination and matrices to solve the system of linear equations. Write your final augmented matrix in triangular form and then solve for each variable using back substitution. -7x - y + 2z = 63 8x + 2z = 74 4y + z = 25

Determine whether the system corresponding to the given augmented matrix is dependent or inconsistent. If it is dependent, give the solution. - $\left[ \begin{array} { r r r | r } 1 & 0 & 0 & 0 \\0 & 1 & 0 & 0 \\0 & 0 & 0 & - 4\end{array} \right]$

Determine the real solutions to the system of nonlinear equations. - +=29 -4x+=17

Determine the real solutions to the system of nonlinear equations. - y=-2x+1 y=-+8x-7

Write the partial fraction decomposition of the rational expression. - $\frac { 7 x ^ { 2 } - 7 x + 3 } { ( x - 1 ) ^ { 3 } }$

Determine the real solutions to the system of nonlinear equations. - +=169 x+y=17

Determine the real solutions to the system of nonlinear equations. - y=+4 y=-+12

Graph the inequality. - $- 2 x - 5 y \leq - 10$ $Graph the inequality. - - 2 x - 5 y \leq - 10$

Determine the real solutions to the system of nonlinear equations. - $- 8 x - y = 9$ $y = x ^ { 2 } - 2$

Graph the system of inequalities. - 4x+3y\geq12 x\geqy $Graph the system of inequalities. - \begin{array} { l } 4 x + 3 y \geq 12 \\ x \geq y \end{array}$

Solve the problem. -Find the dimensions of a rectangle whose perimeter is 48 feet and whose area is 135 square feet.

Graph the system of inequalities. - 2x+3y\geq6 x-y\leq3 x\geq1 $Graph the system of inequalities. - \begin{array}{c} 2 x+3 y \geq 6 \\ x-y \leq 3 \\ x \geq 1 \end{array}$

Solve the system of equations by elimination. - $\frac { 3 } { 5 } x + \frac { 2 } { 5 } y = \frac { 38 } { 5 }$ 6x + 2y = 86

Determine if the ordered pair is a solution to the system of linear inequalities in two variables. - x+y\geq2 -3x+y\leq11 x\geq0 y\geq1

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. -x + 6y = -3 2x + 12y = -6

Graph the inequality. -

Equations, Inequalities, and Applications

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Exam 7: Systems of Equations and Inequalities

Determine the real solutions to the system of nonlinear equations. - y=x-3 =-12x

Solve the system of linear equations. If the system has infinitely many solutions, describe the solution with an ordered triple in terms of variable z. - x+3y+2z =11 4y+9z =-12 x+7y+11z =-1

Determine if each ordered pair is a solution to the given system of inequalities in two variables. - +=61 x+y=-11 (i) (5,6)( 5,6 )(5,6) ; (ii) (6,5)( 6,5 )(6,5)

Graph the inequality. - x4+y3≤1\frac { x } { 4 } + \frac { y } { 3 } \leq 14x​+3y​≤1

Use Gaussian elimination and matrices to solve the system of linear equations. Write your final augmented matrix in triangular form and then solve for each variable using back substitution. -7x - y + 2z = 63 8x + 2z = 74 4y + z = 25

Determine whether the system corresponding to the given augmented matrix is dependent or inconsistent. If it is dependent, give the solution. - [10000100000−4]\left[ \begin{array} { r r r | r } 1 & 0 & 0 & 0 \\0 & 1 & 0 & 0 \\0 & 0 & 0 & - 4\end{array} \right]​100​010​000​00−4​​

Determine the real solutions to the system of nonlinear equations. - +=29 -4x+=17

Determine the real solutions to the system of nonlinear equations. - y=-2x+1 y=-+8x-7

Write the partial fraction decomposition of the rational expression. - 7x2−7x+3(x−1)3\frac { 7 x ^ { 2 } - 7 x + 3 } { ( x - 1 ) ^ { 3 } }(x−1)37x2−7x+3​

Determine the real solutions to the system of nonlinear equations. - +=169 x+y=17

Determine the real solutions to the system of nonlinear equations. - y=+4 y=-+12

Graph the inequality. - −2x−5y≤−10- 2 x - 5 y \leq - 10−2x−5y≤−10

Determine the real solutions to the system of nonlinear equations. - −8x−y=9- 8 x - y = 9−8x−y=9 y=x2−2y = x ^ { 2 } - 2y=x2−2

Graph the system of inequalities. - 4x+3y\geq12 x\geqy

Solve the problem. -Find the dimensions of a rectangle whose perimeter is 48 feet and whose area is 135 square feet.

Graph the system of inequalities. - 2x+3y\geq6 x-y\leq3 x\geq1

Solve the system of equations by elimination. - 35x+25y=385\frac { 3 } { 5 } x + \frac { 2 } { 5 } y = \frac { 38 } { 5 }53​x+52​y=538​ 6x + 2y = 86

Determine if the ordered pair is a solution to the system of linear inequalities in two variables. - x+y\geq2 -3x+y\leq11 x\geq0 y\geq1

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. -x + 6y = -3 2x + 12y = -6

Graph the inequality. -

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

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Determine if each ordered pair is a solution to the given system of inequalities in two variables. - +=61 x+y=-11 (i) $( 5,6 )$ ; (ii) $( 6,5 )$

Graph the inequality. - $\frac { x } { 4 } + \frac { y } { 3 } \leq 1$ $Graph the inequality. - \frac { x } { 4 } + \frac { y } { 3 } \leq 1$

Determine whether the system corresponding to the given augmented matrix is dependent or inconsistent. If it is dependent, give the solution. - $\left[ \begin{array} { r r r | r } 1 & 0 & 0 & 0 \\0 & 1 & 0 & 0 \\0 & 0 & 0 & - 4\end{array} \right]$

Write the partial fraction decomposition of the rational expression. - $\frac { 7 x ^ { 2 } - 7 x + 3 } { ( x - 1 ) ^ { 3 } }$

Graph the inequality. - $- 2 x - 5 y \leq - 10$ $Graph the inequality. - - 2 x - 5 y \leq - 10$

Determine the real solutions to the system of nonlinear equations. - $- 8 x - y = 9$ $y = x ^ { 2 } - 2$

Graph the system of inequalities. - 4x+3y\geq12 x\geqy $Graph the system of inequalities. - \begin{array} { l } 4 x + 3 y \geq 12 \\ x \geq y \end{array}$

Graph the system of inequalities. - 2x+3y\geq6 x-y\leq3 x\geq1 $Graph the system of inequalities. - \begin{array}{c} 2 x+3 y \geq 6 \\ x-y \leq 3 \\ x \geq 1 \end{array}$

Solve the system of equations by elimination. - $\frac { 3 } { 5 } x + \frac { 2 } { 5 } y = \frac { 38 } { 5 }$ 6x + 2y = 86