Question 1

Determine if each ordered pair is a solution to the given system of inequalities in two variables.
-$$\begin{array} { l } 
x y = 56 \
x + y = - 15
\end{array}$$
(i) $( - 8 , - 7 )$; (ii) $( 7,8 )$

Accepted Answer

A)  (i) Yes; (ii) No 
B)  (i) $\mathrm { No }$; (ii) $\mathrm { No }$ 
C)  (i) No; (ii) Yes 
D)  (i) Yes; (ii) Yes 
A)  (i) Yes; (ii) No 
B)  (i) $\mathrm { No }$; (ii) $\mathrm { No }$ 
C)  (i) No; (ii) Yes 
D)  (i) Yes; (ii) Yes

Question 2

Graph the inequality.
-$$x ^ { 2 } + y ^ { 2 } > 4$$

Accepted Answer

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

Question 3

Determine if the ordered pair is a solution to the system of linear inequalities in two variables.
-$$\begin{array} { l } 
x + y \geq 4 \
- 3 x + y \leq 12
\end{array}$$

Accepted Answer

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

Question 4

Solve the system of equations by elimination.
-2x + 36y = -272 9x + 6y = 24

Accepted Answer

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

Question 5

Graph the system of inequalities.
-$\begin{array}{l}
y-x \leq 5 \
x+y \geq 3 \
y-3 x \geq-1
\end{array}$

Accepted Answer

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

Question 6

Solve the system of equations by elimination.
-7x + 64y = 64 4x - 8y = -8

Accepted Answer

A) (1, 1) 
B) (1, 0) 
C) (0, 0) 
D) (0, 1) 
A) (1, 1) 
B) (1, 0) 
C) (0, 0) 
D) (0, 1)

Question 7

Determine whether the system corresponding to the given augmented matrix is dependent or inconsistent. If it is
dependent, give the solution.
-$$\left[ \begin{array} { l l l | l } 
1 & 0 & - 5 & 3 \
0 & 1 & 9 & - 7 \
0 & 0 & 0 & 0
\end{array} \right]$$

Accepted Answer

A)  dependent; $( 3 , - 7 , - 5 )$ 
B)  dependent; $( 3 + 5 z , y = - 7 - 9 z , z )$ 
C)  dependent; $( 3 - 5 z , - 7 + 9 z , z )$ 
D)  inconsistent 
A)  dependent; $( 3 , - 7 , - 5 )$ 
B)  dependent; $( 3 + 5 z , y = - 7 - 9 z , z )$ 
C)  dependent; $( 3 - 5 z , - 7 + 9 z , z )$ 
D)  inconsistent

Question 8

Determine if the ordered pair is a solution to the given inequality.
-$$x + 2 y > 6 ; ( 6,1 )$$

Accepted Answer

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

Question 9

Solve the problem.
-The Little Town Arts Center charges $25 for adults, $14 for senior citizens, and $10 for children under 12 for their live performances on Sunday afternoon. This past Sunday, the paid revenue was $12,800 for 792 tickets sold. There were 41 more children than adults. How many children attended?

Accepted Answer

A) 215 children 
B) 299 children 
C) 268 children 
D) 309 children 
A) 215 children 
B) 299 children 
C) 268 children 
D) 309 children

Question 10

Graph the system of inequalities.
-$\begin{array}{l}
-x+2 y<-8 \
x \geq-1
\end{array}$

Accepted Answer

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

Question 11

A system of nonlinear equations is given. Sketch the graph of the equation of the system and then determine the number of real solutions to the system. Do not solve the system.
-$$\begin{array} { l } 
x ^ { 2 } + y ^ { 2 } = 36 \
x ^ { 2 } + y ^ { 2 } = 4
\end{array}$$

Accepted Answer

A)  Zero
  
B)  Two
  
C)  Two
  
D)  Two
  
A)  Zero
  
B)  Two
  
C)  Two
  
D)  Two

Question 12

Determine if each ordered pair is a solution to the given system of inequalities in two variables.
-$$\begin{array} { l } 
y = x - 1 \
y ^ { 2 } = - 4 x
\end{array}$$
(i) $( - 1 , - 2 )$; (ii) $( 1,0 )$

Accepted Answer

A)  (i) Yes; (ii) Yes 
B)  (i) $\mathrm { No }$; (ii) Yes 
C)  (i) $\mathrm { No }$; (ii) $\mathrm { No }$ 
D)  (i) Yes; (ii) No 
A)  (i) Yes; (ii) Yes 
B)  (i) $\mathrm { No }$; (ii) Yes 
C)  (i) $\mathrm { No }$; (ii) $\mathrm { No }$ 
D)  (i) Yes; (ii) No

Question 13

A system of nonlinear equations is given. Sketch the graph of the equation of the system and then determine the number of real solutions to the system. Do not solve the system.
-$$\begin{array} { l } 
x ^ { 2 } + y ^ { 2 } = 100 \
y - x ^ { 2 } = 0
\end{array}$$

Accepted Answer

A)  Two
  
B)  Two
  
C)  Two
  
D)  One
  
A)  Two
  
B)  Two
  
C)  Two
  
D)  One

Question 14

Determine the real solutions to the system of nonlinear equations.
-$$2 x ^ { 2 } + y ^ { 2 } = 17$$
$3 x ^ { 2 } - 2 y ^ { 2 } = - 6$

Accepted Answer

A)  $( 2,3 ) , ( 2 , - 3 ) , ( - 2,3 ) , ( - 2 , - 3 )$ 
B)  $( 1,3 ) , ( 1 , - 3 ) , ( - 1,3 ) , ( - 1 , - 3 )$ 
C)  $( 1,3 ) , ( - 1 , - 3 )$ 
D)  $( 2 , - 3 ) , ( - 2,3 )$ 
A)  $( 2,3 ) , ( 2 , - 3 ) , ( - 2,3 ) , ( - 2 , - 3 )$ 
B)  $( 1,3 ) , ( 1 , - 3 ) , ( - 1,3 ) , ( - 1 , - 3 )$ 
C)  $( 1,3 ) , ( - 1 , - 3 )$ 
D)  $( 2 , - 3 ) , ( - 2,3 )$

Question 15

Determine if the ordered pair is a solution to the given inequality.
-$$x ^ { 2 } - x y > 49 ; \left( \frac { 5 } { 2 } , - \frac { 7 } { 2 } \right)$$

Accepted Answer

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

Question 16

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

Accepted Answer

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

Question 17

Determine the real solutions to the system of nonlinear equations.
-$$\begin{array} { l } 
x ^ { 2 } + y ^ { 2 } - 4 x + 4 y + 7 = 0 \
x ^ { 2 } - y ^ { 2 } - 4 x - 4 y - 1 = 0
\end{array}$$

Accepted Answer

A)  $( 2 , - 1 ) , ( 2 , - 3 )$ 
B)  $( 2,1 ) , ( 2,3 )$ 
C)  $( 3 , - 2 ) , ( 1 , - 2 )$ 
D)  $( 3 , - 2 ) , ( - 1 , - 2 )$ 
A)  $( 2 , - 1 ) , ( 2 , - 3 )$ 
B)  $( 2,1 ) , ( 2,3 )$ 
C)  $( 3 , - 2 ) , ( 1 , - 2 )$ 
D)  $( 3 , - 2 ) , ( - 1 , - 2 )$

Question 18

Graph the system of inequalities.
-$\begin{array}{l}
y>x^{2} \
4 x+3 y \leq 12
\end{array}$

Accepted Answer

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

Question 19

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.
-$$\begin{aligned}
x + y + z & = 9 \
2 x - 3 y + 4 z & = 7 \
x - 4 y + 3 z & = - 2
\end{aligned}$$

Accepted Answer

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

Question 20

Use Gaussian elimination to solve the linear system by finding an equivalent system in triangular form.
-$$\begin{array} { l } 
5 x + 4 y + z = - 16 \
5 x - 2 y - z = - 2 \
4 x + y + 3 z = 7
\end{array}$$

Accepted Answer

A) (-1, 5, -4) 
B) no solution 
C) (-1, -4, 5) 
D) (5, -4, -1) 
A) (-1, 5, -4) 
B) no solution 
C) (-1, -4, 5) 
D) (5, -4, -1)

Determine if each ordered pair is a solution to the given system of inequalities in two variables. - xy=56 x+y=-15 (i) $( - 8 , - 7 )$ ; (ii) $( 7,8 )$

Graph the inequality. - $x ^ { 2 } + y ^ { 2 } > 4$ $Graph the inequality. - x ^ { 2 } + y ^ { 2 } > 4$

Determine if the ordered pair is a solution to the system of linear inequalities in two variables. - x+y\geq4 -3x+y\leq12

Solve the system of equations by elimination. -2x + 36y = -272 9x + 6y = 24

Graph the system of inequalities. - y-x\leq5 x+y\geq3 y-3x\geq-1 $Graph the system of inequalities. - \begin{array}{l} y-x \leq 5 \\ x+y \geq 3 \\ y-3 x \geq-1 \end{array}$

Solve the system of equations by elimination. -7x + 64y = 64 4x - 8y = -8

Determine whether the system corresponding to the given augmented matrix is dependent or inconsistent. If it is dependent, give the solution. - $\left[ \begin{array} { l l l | l } 1 & 0 & - 5 & 3 \\0 & 1 & 9 & - 7 \\0 & 0 & 0 & 0\end{array} \right]$

Determine if the ordered pair is a solution to the given inequality. - $x + 2 y > 6 ; ( 6,1 )$

Graph the system of inequalities. - -x+2y<-8 x\geq-1 $Graph the system of inequalities. - \begin{array}{l} -x+2 y<-8 \\ x \geq-1 \end{array}$

Determine if each ordered pair is a solution to the given system of inequalities in two variables. - y=x-1 =-4x (i) $( - 1 , - 2 )$ ; (ii) $( 1,0 )$

Determine the real solutions to the system of nonlinear equations. - $2 x ^ { 2 } + y ^ { 2 } = 17$ $3 x ^ { 2 } - 2 y ^ { 2 } = - 6$

Determine if the ordered pair is a solution to the given inequality. - $x ^ { 2 } - x y > 49 ; \left( \frac { 5 } { 2 } , - \frac { 7 } { 2 } \right)$

Graph the system of inequalities. - 2x+3y\geq6 x-y\geq3 y\leq2 $Graph the system of inequalities. - \begin{array}{l} 2 x+3 y \geq 6 \\ x-y \geq 3 \\ y \leq 2 \end{array}$

Determine the real solutions to the system of nonlinear equations. - +-4x+4y+7=0 --4x-4y-1=0

Graph the system of inequalities. - y> 4x+3y\leq12 $Graph the system of inequalities. - \begin{array}{l} y>x^{2} \\ 4 x+3 y \leq 12 \end{array}$

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+y+z =9 2x-3y+4z =7 x-4y+3z =-2

Use Gaussian elimination to solve the linear system by finding an equivalent system in triangular form. - 5x+4y+z=-16 5x-2y-z=-2 4x+y+3z=7

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 each ordered pair is a solution to the given system of inequalities in two variables. - xy=56 x+y=-15 (i) (−8,−7)( - 8 , - 7 )(−8,−7) ; (ii) (7,8)( 7,8 )(7,8)

Graph the inequality. - x2+y2>4x ^ { 2 } + y ^ { 2 } > 4x2+y2>4

Determine if the ordered pair is a solution to the system of linear inequalities in two variables. - x+y\geq4 -3x+y\leq12

Solve the system of equations by elimination. -2x + 36y = -272 9x + 6y = 24

Graph the system of inequalities. - y-x\leq5 x+y\geq3 y-3x\geq-1

Solve the system of equations by elimination. -7x + 64y = 64 4x - 8y = -8

Determine if the ordered pair is a solution to the given inequality. - x+2y>6;(6,1)x + 2 y > 6 ; ( 6,1 )x+2y>6;(6,1)

Graph the system of inequalities. - -x+2y<-8 x\geq-1

A system of nonlinear equations is given. Sketch the graph of the equation of the system and then determine the number of real solutions to the system. Do not solve the system. - +=36 +=4

Determine if each ordered pair is a solution to the given system of inequalities in two variables. - y=x-1 =-4x (i) (−1,−2)( - 1 , - 2 )(−1,−2) ; (ii) (1,0)( 1,0 )(1,0)

A system of nonlinear equations is given. Sketch the graph of the equation of the system and then determine the number of real solutions to the system. Do not solve the system. - +=100 y-=0

Determine the real solutions to the system of nonlinear equations. - 2x2+y2=172 x ^ { 2 } + y ^ { 2 } = 172x2+y2=17 3x2−2y2=−63 x ^ { 2 } - 2 y ^ { 2 } = - 63x2−2y2=−6

Determine if the ordered pair is a solution to the given inequality. - x2−xy>49;(52,−72)x ^ { 2 } - x y > 49 ; \left( \frac { 5 } { 2 } , - \frac { 7 } { 2 } \right)x2−xy>49;(25​,−27​)

Graph the system of inequalities. - 2x+3y\geq6 x-y\geq3 y\leq2

Determine the real solutions to the system of nonlinear equations. - +-4x+4y+7=0 --4x-4y-1=0

Graph the system of inequalities. - y> 4x+3y\leq12

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+y+z =9 2x-3y+4z =7 x-4y+3z =-2

Use Gaussian elimination to solve the linear system by finding an equivalent system in triangular form. - 5x+4y+z=-16 5x-2y-z=-2 4x+y+3z=7

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

Determine if each ordered pair is a solution to the given system of inequalities in two variables. - xy=56 x+y=-15 (i) $( - 8 , - 7 )$ ; (ii) $( 7,8 )$

Graph the inequality. - $x ^ { 2 } + y ^ { 2 } > 4$ $Graph the inequality. - x ^ { 2 } + y ^ { 2 } > 4$

Graph the system of inequalities. - y-x\leq5 x+y\geq3 y-3x\geq-1 $Graph the system of inequalities. - \begin{array}{l} y-x \leq 5 \\ x+y \geq 3 \\ y-3 x \geq-1 \end{array}$

Determine if the ordered pair is a solution to the given inequality. - $x + 2 y > 6 ; ( 6,1 )$

Graph the system of inequalities. - -x+2y<-8 x\geq-1 $Graph the system of inequalities. - \begin{array}{l} -x+2 y<-8 \\ x \geq-1 \end{array}$

Determine if each ordered pair is a solution to the given system of inequalities in two variables. - y=x-1 =-4x (i) $( - 1 , - 2 )$ ; (ii) $( 1,0 )$

Determine the real solutions to the system of nonlinear equations. - $2 x ^ { 2 } + y ^ { 2 } = 17$ $3 x ^ { 2 } - 2 y ^ { 2 } = - 6$

Determine if the ordered pair is a solution to the given inequality. - $x ^ { 2 } - x y > 49 ; \left( \frac { 5 } { 2 } , - \frac { 7 } { 2 } \right)$

Graph the system of inequalities. - 2x+3y\geq6 x-y\geq3 y\leq2 $Graph the system of inequalities. - \begin{array}{l} 2 x+3 y \geq 6 \\ x-y \geq 3 \\ y \leq 2 \end{array}$

Graph the system of inequalities. - y> 4x+3y\leq12 $Graph the system of inequalities. - \begin{array}{l} y>x^{2} \\ 4 x+3 y \leq 12 \end{array}$