Question 1

Determine the real solutions to the system of nonlinear equations.
-$$\begin{array} { l } 
x ^ { 2 } + y ^ { 2 } = 41 \
x - y = 1
\end{array}$$
$x - y = 1$

Accepted Answer

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

Question 2

Graph the inequality.
-

Accepted Answer

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

Question 3

Write the partial fraction decomposition of the rational expression.
-$$\frac { x } { x ^ { 2 } + 11 x + 30 }$$

Accepted Answer

A)  $\frac { - 6 } { x + 6 } + \frac { 5 } { x + 5 }$ 
B)  $\frac { 6 } { x + 6 } + \frac { - 5 } { x + 5 }$ 
C)  $\frac { 6 } { x + 6 } + \frac { 5 } { x + 5 }$ 
D)  $\frac { 5 } { x + 6 } + \frac { - 6 } { x + 5 }$ 
A)  $\frac { - 6 } { x + 6 } + \frac { 5 } { x + 5 }$ 
B)  $\frac { 6 } { x + 6 } + \frac { - 5 } { x + 5 }$ 
C)  $\frac { 6 } { x + 6 } + \frac { 5 } { x + 5 }$ 
D)  $\frac { 5 } { x + 6 } + \frac { - 6 } { x + 5 }$

Question 4

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

Accepted Answer

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

Question 5

Solve the system of equations by substitution.
-3x + y = 13 2x - 7y = 24

Accepted Answer

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

Question 6

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

Accepted Answer

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

Question 7

Determine if each ordered pair is a solution to the given system of inequalities in two variables.
-$$\begin{array} { l } 
x y = 1 \
- 7 x - y = - 8
\end{array}$$
(i) $\left( \frac { 1 } { 7 } , 7 \right)$;(ii) $( 1,1 )$

Accepted Answer

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

Question 8

Graph the system of inequalities.
-$\begin{array}{l}
y2 x-3
\end{array}$

Accepted Answer

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

Question 9

Determine the real solutions to the system of nonlinear equations.
-$$\begin{array} { l } 
2 x ^ { 2 } + y ^ { 2 } = 66 \
x ^ { 2 } + y ^ { 2 } = 41
\end{array}$$

Accepted Answer

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

Question 10

Graph the inequality.
-

Accepted Answer

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

Question 11

Write the partial fraction decomposition of the rational expression.
-$$\frac { - 38 x + 1 } { ( x + 4 ) ^ { 2 } \left( x ^ { 2 } + 1 \right) }$$

Accepted Answer

A)  $\frac { 2 } { x + 4 } + \frac { 8 } { ( x + 4 ) ^ { 2 } } + \frac { - 2 x + 1 } { x ^ { 2 } + 1 }$ 
B)  $\frac { 8 x + 1 } { ( x + 4 ) ^ { 2 } } + \frac { - 2 x - 1 } { x ^ { 2 } + 1 }$ 
C)  $\frac { 2 } { x + 4 } + \frac { 9 } { ( x + 4 ) ^ { 2 } } + \frac { - 2 } { x ^ { 2 } + 1 }$ 
D)  $\frac { 2 } { x + 4 } + \frac { 9 } { ( x + 4 ) ^ { 2 } } + \frac { - 2 x - 1 } { x ^ { 2 } + 1 }$ 
A)  $\frac { 2 } { x + 4 } + \frac { 8 } { ( x + 4 ) ^ { 2 } } + \frac { - 2 x + 1 } { x ^ { 2 } + 1 }$ 
B)  $\frac { 8 x + 1 } { ( x + 4 ) ^ { 2 } } + \frac { - 2 x - 1 } { x ^ { 2 } + 1 }$ 
C)  $\frac { 2 } { x + 4 } + \frac { 9 } { ( x + 4 ) ^ { 2 } } + \frac { - 2 } { x ^ { 2 } + 1 }$ 
D)  $\frac { 2 } { x + 4 } + \frac { 9 } { ( x + 4 ) ^ { 2 } } + \frac { - 2 x - 1 } { x ^ { 2 } + 1 }$

Question 12

Use Gaussian elimination to solve the linear system by finding an equivalent system in triangular form.
-$$\begin{aligned}
x - y + 5 z & = - 5 \
3 x + z & = 0 \
x + 3 y + z & = 15
\end{aligned}$$

Accepted Answer

A) (0, 5, -5) 
B) (0, 0, 5) 
C) no solution 
D) (0, 5, 0) 
A) (0, 5, -5) 
B) (0, 0, 5) 
C) no solution 
D) (0, 5, 0)

Question 13

Solve the system of equations by substitution.
-5x - 2y = -1 x + 4y = 35

Accepted Answer

A) (3, 9) 
B) (2, 8) 
C) (2, 9) 
D) (3, 8) 
A) (3, 9) 
B) (2, 8) 
C) (2, 9) 
D) (3, 8)

Question 14

Determine the real solutions to the system of nonlinear equations.
-$$\ln x = 3 \ln y$$
$$3 ^ { x } = 27 ^ { y }$$

Accepted Answer

A)  $( 3 \sqrt { 3 } , \sqrt { 3 } )$ 
B)  $( \sqrt { 3 } , 9 )$ 
C)  $( \sqrt { 3 } , 3 \sqrt { 3 } )$ 
D)  $( 9 , \sqrt { 3 } )$ 
A)  $( 3 \sqrt { 3 } , \sqrt { 3 } )$ 
B)  $( \sqrt { 3 } , 9 )$ 
C)  $( \sqrt { 3 } , 3 \sqrt { 3 } )$ 
D)  $( 9 , \sqrt { 3 } )$

Question 15

Let x represent one number and let y represent the other number. Use the given conditions to write a system of nonlinear equations. Solve the system and find the numbers.
-The sum of the squares of two numbers is 13. The sum of the two numbers is 5. Find the two numbers.

Accepted Answer

A) -3 and 2; -2 and 3 
B) 2 and 3 
C) 2 and 3; -3 and -2 
D) -3 and -2 
A) -3 and 2; -2 and 3 
B) 2 and 3 
C) 2 and 3; -3 and -2 
D) -3 and -2

Question 16

Graph the inequality.
-$$x ^ { 2 } + y ^ { 2 } \leq 49$$

Accepted Answer

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

Question 17

Graph the inequality.
-

Accepted Answer

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

Question 18

Graph the system of inequalities.
-$$4 x - y \leq 4$$
$$x + 2 y \geq - 8$$

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.
-$$\begin{aligned}
5 x + 2 y + z & = - 11 \
2 x - 3 y - z & = 17 \
7 x - y & = 12
\end{aligned}$$

Accepted Answer

A) no solution 
B) (-2, 0, -1) 
C) (0, -6, 1) 
D) (1, -5, 0) 
A) no solution 
B) (-2, 0, -1) 
C) (0, -6, 1) 
D) (1, -5, 0)

Question 20

Determine the real solutions to the system of nonlinear equations.
-$$\begin{array} { l } 
y = - x ^ { 2 } + 13 \
x ^ { 2 } + y ^ { 2 } = 25
\end{array}$$

Accepted Answer

A)  $( 3,4 ) , ( - 3,4 )$ 
B)  $( 4 , - 3 ) , ( - 4 , - 3 )$ 
C)  $( 9,94 ) , ( 16,269 )$ 
D)  $( 4 , - 3 ) , ( 3,4 ) , ( - 3,4 ) , ( - 4 , - 3 )$ 
A)  $( 3,4 ) , ( - 3,4 )$ 
B)  $( 4 , - 3 ) , ( - 4 , - 3 )$ 
C)  $( 9,94 ) , ( 16,269 )$ 
D)  $( 4 , - 3 ) , ( 3,4 ) , ( - 3,4 ) , ( - 4 , - 3 )$

Determine the real solutions to the system of nonlinear equations. - +=41 x-y=1 $x - y = 1$

Graph the inequality. -

Write the partial fraction decomposition of the rational expression. - $\frac { x } { x ^ { 2 } + 11 x + 30 }$

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

Solve the system of equations by substitution. -3x + y = 13 2x - 7y = 24

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

Determine if each ordered pair is a solution to the given system of inequalities in two variables. - xy=1 -7x-y=-8 (i) $\left( \frac { 1 } { 7 } , 7 \right)$ ;(ii) $( 1,1 )$

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

Determine the real solutions to the system of nonlinear equations. - 2+=66 +=41

Graph the inequality. -

Write the partial fraction decomposition of the rational expression. - $\frac { - 38 x + 1 } { ( x + 4 ) ^ { 2 } \left( x ^ { 2 } + 1 \right) }$

Use Gaussian elimination to solve the linear system by finding an equivalent system in triangular form. - x-y+5z =-5 3x+z =0 x+3y+z =15

Solve the system of equations by substitution. -5x - 2y = -1 x + 4y = 35

Determine the real solutions to the system of nonlinear equations. - $\ln x = 3 \ln y$ $3 ^ { x } = 27 ^ { y }$

Let x represent one number and let y represent the other number. Use the given conditions to write a system of nonlinear equations. Solve the system and find the numbers. -The sum of the squares of two numbers is 13. The sum of the two numbers is 5. Find the two numbers.

Graph the inequality. - $x ^ { 2 } + y ^ { 2 } \leq 49$ $Graph the inequality. - x ^ { 2 } + y ^ { 2 } \leq 49$

Graph the inequality. -

Graph the system of inequalities. - $4 x - y \leq 4$ $x + 2 y \geq - 8$ $Graph the system of inequalities. - 4 x - y \leq 4 x + 2 y \geq - 8$

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. - 5x+2y+z =-11 2x-3y-z =17 7x-y =12

Determine the real solutions to the system of nonlinear equations. - y=-+13 +=25

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 the real solutions to the system of nonlinear equations. - +=41 x-y=1 x−y=1x - y = 1x−y=1

Graph the inequality. -

Write the partial fraction decomposition of the rational expression. - xx2+11x+30\frac { x } { x ^ { 2 } + 11 x + 30 }x2+11x+30x​

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

Solve the system of equations by substitution. -3x + y = 13 2x - 7y = 24

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

Determine if each ordered pair is a solution to the given system of inequalities in two variables. - xy=1 -7x-y=-8 (i) (17,7)\left( \frac { 1 } { 7 } , 7 \right)(71​,7) ;(ii) (1,1)( 1,1 )(1,1)

Graph the system of inequalities. - y<-x+3 y>2x-3

Determine the real solutions to the system of nonlinear equations. - 2+=66 +=41

Graph the inequality. -

Write the partial fraction decomposition of the rational expression. - −38x+1(x+4)2(x2+1)\frac { - 38 x + 1 } { ( x + 4 ) ^ { 2 } \left( x ^ { 2 } + 1 \right) }(x+4)2(x2+1)−38x+1​

Use Gaussian elimination to solve the linear system by finding an equivalent system in triangular form. - x-y+5z =-5 3x+z =0 x+3y+z =15

Solve the system of equations by substitution. -5x - 2y = -1 x + 4y = 35

Determine the real solutions to the system of nonlinear equations. - ln⁡x=3ln⁡y\ln x = 3 \ln ylnx=3lny 3x=27y3 ^ { x } = 27 ^ { y }3x=27y

Let x represent one number and let y represent the other number. Use the given conditions to write a system of nonlinear equations. Solve the system and find the numbers. -The sum of the squares of two numbers is 13. The sum of the two numbers is 5. Find the two numbers.

Graph the inequality. - x2+y2≤49x ^ { 2 } + y ^ { 2 } \leq 49x2+y2≤49

Graph the inequality. -

Graph the system of inequalities. - 4x−y≤44 x - y \leq 44x−y≤4 x+2y≥−8x + 2 y \geq - 8x+2y≥−8

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. - 5x+2y+z =-11 2x-3y-z =17 7x-y =12

Determine the real solutions to the system of nonlinear equations. - y=-+13 +=25

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 the real solutions to the system of nonlinear equations. - +=41 x-y=1 $x - y = 1$

Write the partial fraction decomposition of the rational expression. - $\frac { x } { x ^ { 2 } + 11 x + 30 }$

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

Determine if each ordered pair is a solution to the given system of inequalities in two variables. - xy=1 -7x-y=-8 (i) $\left( \frac { 1 } { 7 } , 7 \right)$ ;(ii) $( 1,1 )$

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

Write the partial fraction decomposition of the rational expression. - $\frac { - 38 x + 1 } { ( x + 4 ) ^ { 2 } \left( x ^ { 2 } + 1 \right) }$

Determine the real solutions to the system of nonlinear equations. - $\ln x = 3 \ln y$ $3 ^ { x } = 27 ^ { y }$

Graph the inequality. - $x ^ { 2 } + y ^ { 2 } \leq 49$ $Graph the inequality. - x ^ { 2 } + y ^ { 2 } \leq 49$

Graph the system of inequalities. - $4 x - y \leq 4$ $x + 2 y \geq - 8$ $Graph the system of inequalities. - 4 x - y \leq 4 x + 2 y \geq - 8$