Question 1

Solve the system of equations by using the addition method.
-$$\begin{array} { l } 
3 x ^ { 2 } - 4 y ^ { 2 } = - 5 \
3 x ^ { 2 } - 2 y ^ { 2 } = 11
\end{array}$$

Accepted Answer

A)  $\{ ( 9,8 ) \}$ 
B)  $\{ ( 3,2 \sqrt { 2 } ) \}$ 
C)  $\{ ( 9,8 ) , ( 9 , - 8 ) , ( - 9,8 ) , ( - 9 , - 8 ) \}$ 
D)  $\{ ( 3,2 \sqrt { 2 } ) , ( 3 , - 2 \sqrt { 2 } ) , ( - 3,2 \sqrt { 2 } ) , ( - 3 , - 2 \sqrt { 2 } ) \}$ 
A)  $\{ ( 9,8 ) \}$ 
B)  $\{ ( 3,2 \sqrt { 2 } ) \}$ 
C)  $\{ ( 9,8 ) , ( 9 , - 8 ) , ( - 9,8 ) , ( - 9 , - 8 ) \}$ 
D)  $\{ ( 3,2 \sqrt { 2 } ) , ( 3 , - 2 \sqrt { 2 } ) , ( - 3,2 \sqrt { 2 } ) , ( - 3 , - 2 \sqrt { 2 } ) \}$

Question 2

Solve the system by using any method.
-$\begin{array} { l } 
\frac { 8 } { x ^ { 2 } } - \frac { 1 } { y ^ { 2 } } = - 7 \
\frac { 4 } { x ^ { 2 } } + \frac { 2 } { y ^ { 2 } } = 19
\end{array}$

Accepted Answer

A)  {  } 
B)  $\left\{ \left( 2 , \frac { 1 } { 3 } \right) \right\}$ 
C)  $\left\{ \left( - 2 , \frac { 1 } { 3 } \right) , \left( - 2 , - \frac { 1 } { 3 } \right) , \left( 2 , \frac { 1 } { 3 } \right) , \left( 2 , - \frac { 1 } { 3 } \right) \right\}$ 
D)  $\left\{ \left( 2 , \frac { 1 } { 3 } \right) , \left( 2 , - \frac { 1 } { 3 } \right) \right\}$ 
A)  {  } 
B)  $\left\{ \left( 2 , \frac { 1 } { 3 } \right) \right\}$ 
C)  $\left\{ \left( - 2 , \frac { 1 } { 3 } \right) , \left( - 2 , - \frac { 1 } { 3 } \right) , \left( 2 , \frac { 1 } { 3 } \right) , \left( 2 , - \frac { 1 } { 3 } \right) \right\}$ 
D)  $\left\{ \left( 2 , \frac { 1 } { 3 } \right) , \left( 2 , - \frac { 1 } { 3 } \right) \right\}$

Question 3

Solve the system. If a system has one unique solution, write the solution set. Otherwise, determine the number of solutions to the system, and determine whether the system is inconsistent, or the equations are dependent.
-$$\begin{aligned}
x - \frac { 3 } { 4 } y + \frac { 5 } { 4 } z & = \frac { 15 } { 4 } \
- \frac { 1 } { 4 } x + \frac { 1 } { 2 } y + \frac { 1 } { 8 } z & = - \frac { 19 } { 8 } \
- \frac { 5 } { 2 } x + \frac { 9 } { 2 } y + z & = - 21
\end{aligned}$$

Accepted Answer

A)  No solution; inconsistent 
B)  $\{ ( - 2 , - 6,1 ) \}$ 
C)  $\{ ( 0,0,0 ) \}$ 
D)  $\{ ( 2,1,2 ) \}$ 
A)  No solution; inconsistent 
B)  $\{ ( - 2 , - 6,1 ) \}$ 
C)  $\{ ( 0,0,0 ) \}$ 
D)  $\{ ( 2,1,2 ) \}$

Question 4

Solve the system of equations by using the addition method.
-$$\begin{array} { l } 
0.6 x + 0.1 y = 0.3 \
3 x - 0.4 y = 0.6
\end{array}$$

Accepted Answer

A)  $\{ ( 1,1 ) \}$ 
B)  $\left\{ \left( \frac { 1 } { 3 } , 1 \right) \right\}$ 
C)  $\{ ( 0,3 ) \}$ 
D)  $\{ ( 1 , - 24 ) \}$ 
A)  $\{ ( 1,1 ) \}$ 
B)  $\left\{ \left( \frac { 1 } { 3 } , 1 \right) \right\}$ 
C)  $\{ ( 0,3 ) \}$ 
D)  $\{ ( 1 , - 24 ) \}$

Question 5

Graph the solution set.
-$$\begin{array} { l } 
y \leq - 2 x + 5 \
y \geq \frac { 3 } { 2 } x - 2
\end{array}$$

Accepted Answer

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

Question 6

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
-The process of decomposing a rational expression into two or more simpler fractions is called________partial .

Accepted Answer

fraction d

Question 7

Solve the system by the substitution method.
-$$\begin{array} { l } 
y = x ^ { 2 } + 1 \
- 4 x - y = 2
\end{array}$$

Accepted Answer

A)  $\{ ( - 1,2 ) , ( - 3,10 ) \}$ 
B)  \{ \} 
C)  $\{ ( 1,2 ) , ( - 1,2 ) \}$ 
D)  $( 0,1 ) , ( 0 , - 2 ) \}$ 
A)  $\{ ( - 1,2 ) , ( - 3,10 ) \}$ 
B)  \{ \} 
C)  $\{ ( 1,2 ) , ( - 1,2 ) \}$ 
D)  $( 0,1 ) , ( 0 , - 2 ) \}$

Question 8

Determine whether the ordered pair is a solution to the system of inequalities.
-$$\begin{array} { l } 
y < - x ^ { 2 } + 4 ; \quad ( 0,1 ) \
x + 2 y \leq 2
\end{array}$$

Accepted Answer

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

Question 9

Solve the problem.
-The attending physician in an emergency room treats an unconscious patient suspected of a drug overdose. The physician does not know the initial concentration $A _ { 0 }$ of the drug in the bloodstream at the time of injection. However, the physician knows that after $3 \mathrm { hr }$, the drug concentration in the blood is $0.75 \mu \mathrm { g } / \mathrm { dL }$ and after $4 \mathrm { hr }$, the concentration is $0.719 \mu \mathrm { g } / \mathrm { dL }$. The model $A ( t ) = A _ { 0 } \mathrm { e } ^ { - k t }$ represents the drug concentration $A ( t )$ (in $\mu \mathrm { g } / \mathrm { dL } )$ in the bloodstream $t$ hours after injection. The value of $k$ is a constant related to the rate at which the drug is removed by the body.

Accepted Answer

A)  a. $0.75 = A _ { 0 } \mathrm { e } ^ { 3 t }$
b. $0.719 = A _ { 0 } \mathrm { e } ^ { 4 t }$
c. $k = 0.042$ 
B)  a. $0.75 = A _ { 0 } \mathrm { e } ^ { - 3 t }$
b. $0.719 = A _ { 0 } \mathrm { e } ^ { - 4 t }$
c. $k = 0.618$ 
C)  a. $0.75 = A _ { 0 } \mathrm { e } ^ { - 3 t }$
b. $0.719 = A _ { 0 } \mathrm { e } ^ { - 4 t }$
c. $k = 0.042$ 
D)  a. $0.75 = A _ { 0 } \mathrm { e } ^ { 3 t }$
b. $0.719 = A _ { 0 } \mathrm { e } ^ { 4 t }$
c. $k = 0.618$ 
A)  a. $0.75 = A _ { 0 } \mathrm { e } ^ { 3 t }$
b. $0.719 = A _ { 0 } \mathrm { e } ^ { 4 t }$
c. $k = 0.042$ 
B)  a. $0.75 = A _ { 0 } \mathrm { e } ^ { - 3 t }$
b. $0.719 = A _ { 0 } \mathrm { e } ^ { - 4 t }$
c. $k = 0.618$ 
C)  a. $0.75 = A _ { 0 } \mathrm { e } ^ { - 3 t }$
b. $0.719 = A _ { 0 } \mathrm { e } ^ { - 4 t }$
c. $k = 0.042$ 
D)  a. $0.75 = A _ { 0 } \mathrm { e } ^ { 3 t }$
b. $0.719 = A _ { 0 } \mathrm { e } ^ { 4 t }$
c. $k = 0.618$

Question 10

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
-The solution set to the system of inequalities x  0 represents the points in Quadrant (I, II, III,
IV).

Accepted Answer

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

Question 11

Determine the values of x and y that produce the minimum value of the objective function on the feasible
region. Determine the minimum value of the objective function on the feasible region.
-$$\begin{array} { l } 
x \geq 0 , y \geq 0 \
40 x + 30 y \geq 3,200 \
x \geq 1.75 y \
\quad \text { Minimize } z = 22 x + 12 y
\end{array}$$

Accepted Answer

A)  $x = 32 , y = 56$; Minimum value: 48,320 
B)  $x = 32 , y = 56$; Minimum value: 1,376 
C)  $x = 56 , y = 32$; Minimum value: 60,800 
D)  $x = 56 , y = 32$; Minimum value: 1,616 
A)  $x = 32 , y = 56$; Minimum value: 48,320 
B)  $x = 32 , y = 56$; Minimum value: 1,376 
C)  $x = 56 , y = 32$; Minimum value: 60,800 
D)  $x = 56 , y = 32$; Minimum value: 1,616

Question 12

Solve the system by using any method. If a system does not have one unique solution, state whether the
system is inconsistent or whether the equations are dependent.
-$$\begin{array} { l } 
5 x + y = - 5 \
- 15 x - 3 y = 9
\end{array}$$

Accepted Answer

A)  { } ; The system is inconsistent. 
B)  $\{ ( 1 , - 10 ) \}$ 
C)  $\{ ( x , y ) \mid 5 x + y = - 5 \}$; The equations are dependent. 
D)  $\{ ( 0 , - 5 ) \}$ 
A)  { } ; The system is inconsistent. 
B)  $\{ ( 1 , - 10 ) \}$ 
C)  $\{ ( x , y ) \mid 5 x + y = - 5 \}$; The equations are dependent. 
D)  $\{ ( 0 , - 5 ) \}$

Question 13

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.
-$\frac { 6 x + 5 } { ( 2 x - 5 ) ( x + 4 ) }$

Accepted Answer

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

Question 14

Determine which point is the solution to the given system.
-$$\begin{array} { l } 
y = - 2 x + 6 \
y = 2 x - 18
\end{array}$$

Accepted Answer

A)  $( - 8,22 )$ 
B)  $( 8 , - 10 )$ 
C)  $( 6 , - 6 )$ 
D)  $( 2,2 )$ 
A)  $( - 8,22 )$ 
B)  $( 8 , - 10 )$ 
C)  $( 6 , - 6 )$ 
D)  $( 2,2 )$

Question 15

Solve the problem.
-Stuart pays back two student loans over a 4 -yr period. One loan charges the equivalent of $3 \%$ simple interest and the other charges the equivalent of $5.5 \%$ simple interest. If the total amount borrowed was $\$ 32,000$ and the total amount of interest paid after 4 yr is $\$ 4,640$, find the amount borrowed from each loan.

Accepted Answer

A)  11,000 at $3 \%$ and 21,000 at $5.5 \%$ 
B)  8,000 at $3 \%$ and 24,000 at $5.5 \%$ 
C)  24,000 at $3 \%$ and 8,000 at $5.5 \%$ 
D)  21,000 at $3 \%$ and 11,000 at $5.5 \%$ 
A)  11,000 at $3 \%$ and 21,000 at $5.5 \%$ 
B)  8,000 at $3 \%$ and 24,000 at $5.5 \%$ 
C)  24,000 at $3 \%$ and 8,000 at $5.5 \%$ 
D)  21,000 at $3 \%$ and 11,000 at $5.5 \%$

Question 16

Solve the system by using any method. If a system does not have one unique solution, state whether the
system is inconsistent or whether the equations are dependent.
-$$\begin{array} { l } 
y = 0.4 x + 2.06 \
y = - 3.6 x - 5.54
\end{array}$$

Accepted Answer

A)  $\{ ( 3 , - 16.34 ) \}$ 
B)  $\{ ( 1.3,2.58 ) \}$ 
C)  $\{ ( - 2,1.26 ) \}$ 
D)  $\{ ( - 1.9,1.3 ) \}$ 
A)  $\{ ( 3 , - 16.34 ) \}$ 
B)  $\{ ( 1.3,2.58 ) \}$ 
C)  $\{ ( - 2,1.26 ) \}$ 
D)  $\{ ( - 1.9,1.3 ) \}$

Question 17

Solve the system by substitution.
-$$\begin{aligned}
x + 4 y & = 6 \
3 x - 5 y & = - 16
\end{aligned}$$

Accepted Answer

A)  $\{ ( 2,1 ) \}$ 
B)  $\{ ( 6,0 ) \}$ 
C)  $\{ ( 10 , - 1 ) \}$ 
D)  $\{ ( - 2,2 ) \}$ 
A)  $\{ ( 2,1 ) \}$ 
B)  $\{ ( 6,0 ) \}$ 
C)  $\{ ( 10 , - 1 ) \}$ 
D)  $\{ ( - 2,2 ) \}$

Question 18

Solve the problem.
-A fishing boat travels 36 mi with the current in 2 hr. It travels 42 mi against the current in 3 hr. Find the speed of the boat in still water.

Accepted Answer

A)  The boat travels 2 mph in still water. 
B)  The boat travels 14 mph in still water. 
C)  The boat travels 18 mph in still water. 
D)  The boat travels 16 mph in still water. 
A)  The boat travels 2 mph in still water. 
B)  The boat travels 14 mph in still water. 
C)  The boat travels 18 mph in still water. 
D)  The boat travels 16 mph in still water.

Question 19

Identify the system for which the ordered triple is a solution.
-$$( - 5 , - 4,4 )$$

Accepted Answer

A)  $5 x - 3 y - 4 z = - 29$
$- 4 x + 3 y + 5 z = 28$ 
$- 3 x - 5 y + 2 z = 27$ 
B)  $5 x + 3 y - 4 z = - 53$
$- 4 x + 3 y + 5 z = 28$
$- 3 x - 5 y + 2 z = 27$ 
C)  $5 x - 3 y - 4 z = - 29$
$- 4 x - 3 y + 5 z = 52$
$- 3 x - 5 y - 2 z = 27$ 
D)  $5 x + 3 y - 4 z = - 53$
$- 4 x - 3 y - 5 z = 52$
$- 3 x - 5 y - 2 z = 27$ 
A)  $5 x - 3 y - 4 z = - 29$
$- 4 x + 3 y + 5 z = 28$ 
$- 3 x - 5 y + 2 z = 27$ 
B)  $5 x + 3 y - 4 z = - 53$
$- 4 x + 3 y + 5 z = 28$
$- 3 x - 5 y + 2 z = 27$ 
C)  $5 x - 3 y - 4 z = - 29$
$- 4 x - 3 y + 5 z = 52$
$- 3 x - 5 y - 2 z = 27$ 
D)  $5 x + 3 y - 4 z = - 53$
$- 4 x - 3 y - 5 z = 52$
$- 3 x - 5 y - 2 z = 27$

Question 20

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
-In what situation should long division be used before attempting to decompose a rational expression
into partial fractions?

Accepted Answer

When the degree of the numerat

Solve the system of equations by using the addition method. - 3-4=-5 3-2=11

Solve the system by using any method. - -=-7 +=19

Solve the system. If a system has one unique solution, write the solution set. Otherwise, determine the number of solutions to the system, and determine whether the system is inconsistent, or the equations are dependent. - x-y+z = -x+y+z =- -x+y+z =-21

Solve the system of equations by using the addition method. - 0.6x+0.1y=0.3 3x-0.4y=0.6

Graph the solution set. - y\leq-2x+5 y\geqx-2

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -The process of decomposing a rational expression into two or more simpler fractions is called________partial .

Solve the system by the substitution method. - y=+1 -4x-y=2

Determine whether the ordered pair is a solution to the system of inequalities. - y<-+4;(0,1) x+2y\leq2

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -The solution set to the system of inequalities x < 0, y > 0 represents the points in Quadrant (I, II, III, IV).

Determine the values of x and y that produce the minimum value of the objective function on the feasible region. Determine the minimum value of the objective function on the feasible region. - x\geq0,y\geq0 40x+30y\geq3,200 x\geq1.75y Minimize z=22x+12y

Solve the system by using any method. If a system does not have one unique solution, state whether the system is inconsistent or whether the equations are dependent. - 5x+y=-5 -15x-3y=9

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. - $\frac { 6 x + 5 } { ( 2 x - 5 ) ( x + 4 ) }$

Determine which point is the solution to the given system. - y=-2x+6 y=2x-18

Solve the system by using any method. If a system does not have one unique solution, state whether the system is inconsistent or whether the equations are dependent. - y=0.4x+2.06 y=-3.6x-5.54

Solve the system by substitution. - x+4y =6 3x-5y =-16

Solve the problem. -A fishing boat travels 36 mi with the current in 2 hr. It travels 42 mi against the current in 3 hr. Find the speed of the boat in still water.

Identify the system for which the ordered triple is a solution. - $( - 5 , - 4,4 )$

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -In what situation should long division be used before attempting to decompose a rational expression into partial fractions?

Equations and Inequalities

Functions and Relations

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Matrices and Determinants and Applications

Analytic Geometry

Sequences, Series, Induction, and Probability

Review of Prerequisites

Filters

Exam 5: Systems of Equations and Inequalities