Question 1

Solve the system of equations by using the addition method.
-$$\begin{array} { l } 
x ^ { 2 } - x y = - 3 \
2 x ^ { 2 } + 3 x y = 14
\end{array}$$

Accepted Answer

A)  $\{ ( - 1 , - 4 ) , ( 1,4 ) \}$ 
B)  $\{ ( 1,4 ) , ( 1 , - 4 ) , ( - 1,4 ) , ( - 1 , - 4 ) \}$ 
C)  $\{ ( 1,4 ) , ( 1 , - 4 ) \}$ 
D) {  }

Question 2

Solve the system by using any method.
-$$\begin{array} { l } 
y = x \
y = \frac { 1 } { x ^ { 2 } }
\end{array}$$

Accepted Answer

A)  $\{ ( - 1 , - 1 ) \}$ 
B)  $\{ ( 1,1 ) \}$ 
C)  $\{ ( - 1 , - 1 ) , ( 1,1 ) \}$ 
D) {  }

Question 3

Choose the one alternative that best completes the statement or answers the question.
Determine whether the ordered pair is a solution to the inequality.
-$$y \leq - x ^ { 2 } + 2$$

Accepted Answer

A) 
 
B) 
 
C) 
 
D)

Question 4

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
-The function to be optimized in a linear programming application is called the________function.

Accepted Answer

The answer of Write the word or phrase that best...

Question 5

Find the partial fraction decomposition.
-$$\frac { x ^ { 4 } + 5 x ^ { 3 } + 6 x ^ { 2 } + 27 x - 10 } { x ^ { 3 } + 5 x }$$

Accepted Answer

A)  $x - 5 + \frac { - 2 } { x } + \frac { 3 x } { x ^ { 2 } + 5 }$ 
B)  $\frac { - 2 } { x } + \frac { 3 x + 2 } { x ^ { 2 } + 5 }$ 
C)  $x + 5 + \frac { - 2 } { x } + \frac { 3 x + 2 } { x ^ { 2 } + 5 }$ 
D)  $\frac { - 2 } { x } + \frac { 3 x } { x ^ { 2 } + 5 }$

Question 6

Choose the one alternative that best completes the statement or answers the question.
Determine whether the ordered pair is a solution to the inequality.
-$$- 3 x + 4 y \geq - 12$$

Accepted Answer

A) 
 
B) 
 
C) 
 
D)

Question 7

Find the partial fraction decomposition.
-$$\frac { 4 x ^ { 3 } + 15 x ^ { 2 } + 15 x + 6 } { x ^ { 2 } + 4 x + 4 }$$

Accepted Answer

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

Question 8

Solve the problem.
-The ratio of two numbers is 2 to 3 and the sum of their squares is 52. Find the numbers.

Accepted Answer

A)  The numbers are 4 and 6. 
B)  The numbers are 4 and 6 or -4 and -6. 
C)  The numbers are 6 and 9 or -6 and -9. 
D)  The numbers are 6 and 9.

Question 9

Solve the problem.
-Find $C$ and $D$ so that the solution set to the system is $\{ ( - 4,2 ) \}$.
$$\begin{array} { l } 
C x - 2 y = - 16 \
2 x + D y = - 16
\end{array}$$

Accepted Answer

A)  $C = - 4 ; \mathrm { D } = - 3$ 
B)  $C = 3 ; \mathrm { D } = - 4$ 
C)  $C = - 3 ; \mathrm { D } = 4$ 
D)  $C = - 4 ; \mathrm { D } = 3$

Question 10

Choose the one alternative that best completes the statement or answers the question.
Set up the form for the partial fraction decomposition. Do not solve for A, B, C, and so on.
-$$\frac { x ^ { 2 } + 3 x + 4 } { x ^ { 3 } + 5 x ^ { 2 } - 36 x }$$

Accepted Answer

A)  $\frac { A } { x } + \frac { B } { x + 9 } + \frac { C } { x - 4 }$ 
B)  $\frac { A } { x ^ { 3 } } + \frac { B } { 5 x ^ { 2 } } - \frac { C } { 36 x ^ { 2 } }$ 
C)  $\frac { A } { x ^ { 3 } } + \frac { B x + C } { 5 x ^ { 2 } } - \frac { D x + E } { 36 x ^ { 2 } }$ 
D)  $\frac { A } { x } + \frac { B x + C } { x + 9 } + \frac { D x + E } { x - 4 }$

Question 11

A system of equations is given in which each question is written in slope-intercept form. Determine the
number of solutions. If the system does not have one unique solution, state whether the system is
inconsistent or whether the equations are dependent.
-$$\begin{array} { l } 
y = \frac { 9 } { 4 } x - 5 \
y = \frac { 9 } { 4 } x - 5
\end{array}$$

Accepted Answer

A)  One solution 
B)  Infinitely many solutions; The equations are dependent. 
C)  No solution; The system is inconsistent.

Question 12

Solve the system of equations by using the substitution method.
-$$\begin{array} { l } 
- 5 x = - 2 y - 9 \
- 1 - 5 x = 4
\end{array}$$

Accepted Answer

A)  $\{ ( - 1 , - 2 ) \}$ 
B)  $\{ ( 1 , - 2 ) \}$ 
C)  $\{ ( - 1 , - 7 ) \}$ 
D)  $\{ ( - 1,14 ) \}$

Question 13

Use a graphing utility to approximate the solution(s) to the system of equations. Round the coordinates to 3 decimal places.
-$$\begin{array} { l } 
x ^ { 2 } + y ^ { 2 } = 35 \
y = - x ^ { 2 } + 7.6
\end{array}$$

Accepted Answer

A)  $\{ ( 1.357 , - 5.758 \} , \{ 3.515,4.758 \} )$ 
B)  $\{ ( 1.357,5.758 \} , \{ - 1.357,5.758 \} , \{ 3.515 , - 4.758 \} , \{ - 3.515 , - 4.758 \} )$ 
C)  $\{ ( 1.357,5.758 \} , \{ 3.515 , - 4.758 \} )$ 
D)  $\{ ( 1.357,5.758 \} , \{ 1.357 , - 5.758 \} , \{ 3.515 , - 4.758 \} , \{ 3.515,4.758 \} )$

Question 14

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
-An inequality that can be written in the form Ax + By < C (where A and B are not both zero) is called a inequality in two variables.

Accepted Answer

The answer of Write the word or phrase that best...

Question 15

Solve the system by using any method.
-$$\begin{array} { l } 
4 = 2 \lambda x \
10 = 2 \lambda y \
x ^ { 2 } + y ^ { 2 } = 29
\end{array}$$

Accepted Answer

A)  $\{ ( 1,1,5 ) , ( - 1 , - 1 , - 5 ) \}$ 
B)  $\{ ( 1,1,2 ) \}$ 
C)  $\{ ( 1,1,2 ) , ( - 1 , - 1 , - 2 ) \}$ 
D)  $\{ ( 2,5,1 ) , ( - 2 , - 5 , - 1 ) \}$

Exam 5: Systems of Equations and Inequalities

Solve the system of equations by using the addition method. - $\begin{array} { l } x ^ { 2 } - x y = - 3 \\2 x ^ { 2 } + 3 x y = 14\end{array}$

Solve the system by using any method. - $\begin{array} { l } y = x \\y = \frac { 1 } { x ^ { 2 } }\end{array}$

Choose the one alternative that best completes the statement or answers the question. Determine whether the ordered pair is a solution to the inequality. - $y \leq - x ^ { 2 } + 2$

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -The function to be optimized in a linear programming application is called the________function.

Find the partial fraction decomposition. - $\frac { x ^ { 4 } + 5 x ^ { 3 } + 6 x ^ { 2 } + 27 x - 10 } { x ^ { 3 } + 5 x }$

Choose the one alternative that best completes the statement or answers the question. Determine whether the ordered pair is a solution to the inequality. - $- 3 x + 4 y \geq - 12$

Find the partial fraction decomposition. - $\frac { 4 x ^ { 3 } + 15 x ^ { 2 } + 15 x + 6 } { x ^ { 2 } + 4 x + 4 }$

Solve the problem. -The ratio of two numbers is 2 to 3 and the sum of their squares is 52. Find the numbers.

Solve the problem. -Find $C$ and $D$ so that the solution set to the system is $\{ ( - 4,2 ) \}$ . $\begin{array} { l } C x - 2 y = - 16 \\2 x + D y = - 16\end{array}$

Choose the one alternative that best completes the statement or answers the question. Set up the form for the partial fraction decomposition. Do not solve for A, B, C, and so on. - $\frac { x ^ { 2 } + 3 x + 4 } { x ^ { 3 } + 5 x ^ { 2 } - 36 x }$

Solve the system of equations by using the substitution method. - $\begin{array} { l } - 5 x = - 2 y - 9 \\- 1 - 5 x = 4\end{array}$

Use a graphing utility to approximate the solution(s) to the system of equations. Round the coordinates to 3 decimal places. - $\begin{array} { l } x ^ { 2 } + y ^ { 2 } = 35 \\y = - x ^ { 2 } + 7.6\end{array}$

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -An inequality that can be written in the form Ax + By < C (where A and B are not both zero) is called a inequality in two variables.

Solve the system by using any method. - $\begin{array} { l } 4 = 2 \lambda x \\10 = 2 \lambda y \\x ^ { 2 } + y ^ { 2 } = 29\end{array}$

Exam 5: Systems of Equations and Inequalities

Solve the system of equations by using the addition method. - x2−xy=−32x2+3xy=14\begin{array} { l } x ^ { 2 } - x y = - 3 \\2 x ^ { 2 } + 3 x y = 14\end{array}x2−xy=−32x2+3xy=14​

Solve the system by using any method. - y=xy=1x2\begin{array} { l } y = x \\y = \frac { 1 } { x ^ { 2 } }\end{array}y=xy=x21​​

Choose the one alternative that best completes the statement or answers the question. Determine whether the ordered pair is a solution to the inequality. - y≤−x2+2y \leq - x ^ { 2 } + 2y≤−x2+2

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -The function to be optimized in a linear programming application is called the________function.

Find the partial fraction decomposition. - x4+5x3+6x2+27x−10x3+5x\frac { x ^ { 4 } + 5 x ^ { 3 } + 6 x ^ { 2 } + 27 x - 10 } { x ^ { 3 } + 5 x }x3+5xx4+5x3+6x2+27x−10​

Choose the one alternative that best completes the statement or answers the question. Determine whether the ordered pair is a solution to the inequality. - −3x+4y≥−12- 3 x + 4 y \geq - 12−3x+4y≥−12

Find the partial fraction decomposition. - 4x3+15x2+15x+6x2+4x+4\frac { 4 x ^ { 3 } + 15 x ^ { 2 } + 15 x + 6 } { x ^ { 2 } + 4 x + 4 }x2+4x+44x3+15x2+15x+6​