Question 1

Determine whether the ordered pair or ordered triple satisfies the system of linear equations.
-$$\begin{array} { l } 
y = - 3 x - 7 \
y = - \frac { 4 } { 3 } x - \frac { 1 } { 3 } \
( - 4 , - 5 )
\end{array}$$

Accepted Answer

A) not a solution 
B) solution 
A) not a solution 
B) solution

Question 2

Solve the problem.
-Jancie has $180,000 to invest to obtain annual income. She wants some of it invested in safe Certificates of Deposit yielding 7%. The rest she wants to invest in AA bonds yielding 11% per year. How much should she
Invest in each to realize exactly $17,400 per year?

Accepted Answer

A) $120,000 at 7% and $60,000 at 11% 
B) $120,000 at 11% and $60,000 at 7% 
C) $110,000 at 7% and $70,000 at 11% 
D) $130,000 at 11% and $50,000 at 7% 
A) $120,000 at 7% and $60,000 at 11% 
B) $120,000 at 11% and $60,000 at 7% 
C) $110,000 at 7% and $70,000 at 11% 
D) $130,000 at 11% and $50,000 at 7%

Question 3

Determine the solution to the system of inequalities.
-$\begin{array} { l } 
y < 2 x + 2 \
y \leq - \frac { 3 } { 2 } x
\end{array}$

Accepted Answer

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

Question 4

Evaluate the determinant.
-$$\left| \begin{array} { l l l } 
1 & 2 & 5 \
2 & 4 & 3 \
1 & 2 & 5
\end{array} \right|$$

Accepted Answer

A) 92 
B) 1 
C) 0 
D) -12 
A) 92 
B) 1 
C) 0 
D) -12

Question 5

Solve the system of equations using the addition method.
-$$\begin{array} { l } 
- 0.2 x + 0.3 y - 0.3 z = - 2.8 \
0.4 x - 0.1 y + 0.2 z = 2 \
- 0.2 x - 0.4 y + 0.4 z = 2.8
\end{array}$$

Accepted Answer

A) (2, -4, 4) 
B) (-0.6, 8, 5) 
C) (-0.6, 10, 4) 
D) (-0.4, 10, 5) 
A) (2, -4, 4) 
B) (-0.6, 8, 5) 
C) (-0.6, 10, 4) 
D) (-0.4, 10, 5)

Question 6

Solve the system of equations using the addition method.
-$$\begin{array} { r } 
5 x + 35 y = 35 \
9 x - 5 y = - 5
\end{array}$$

Accepted Answer

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

Question 7

Determine the solution to the system of inequalities.
-$\begin{array} { l } 
x \geq 0 \
y \geq 0 \
2 x + 2 y \leq 4 \
3 x + y \leq 5 \
\end{array}$

Accepted Answer

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

Question 8

Solve the problem.
-The sum of the measures of the angles of a triangle is 180°. The smallest angle of the triangle has a measuree $$\frac { 3 } { 5 }$$ the measure of the second smallest angle. The largest angle is 9° less than eleven times the measure of the second smallest angle. Determine the measure of each angle.

Accepted Answer

A) smallest angle: 3° 
B) smallest angle: 18° second smallest angle: 15° second smallest angle: 30°
Largest angle: 162° largest angle: 132° 
C) smallest angle: 7.2° 
D) smallest angle: 9° second smallest angle: 12° second smallest angle: 15°
Largest angle: 160.8° largest angle: 156° 
A) smallest angle: 3° 
B) smallest angle: 18° second smallest angle: 15° second smallest angle: 30°
Largest angle: 162° largest angle: 132° 
C) smallest angle: 7.2° 
D) smallest angle: 9° second smallest angle: 12° second smallest angle: 15°
Largest angle: 160.8° largest angle: 156°

Question 9

Determine the solution to the system of equations graphically. If the system is inconsistent or dependent, so state.
-$$\begin{array} { l } 
y = - 3 x - 1 \
- 6 x - 2 y = 2
\end{array}$$

Accepted Answer

A) (0, -1) 
B) (0, 0) 
C) dependent 
D) inconsistent 
A) (0, -1) 
B) (0, 0) 
C) dependent 
D) inconsistent

Question 10

Solve the system of equations using determinants.
-$$\begin{array} { l } 
- 4 x - 2 y = - 18 \
- 8 x = - 20 + 4 y
\end{array}$$

Accepted Answer

A) (2, 5) 
B) (-3, -1) 
C) (2, -1) 
D) no solution 
A) (2, 5) 
B) (-3, -1) 
C) (2, -1) 
D) no solution

Question 11

Determine the solution to the system of inequalities.
-$\begin{array} { l } 
| y | > 6 \
y \leq x - 3
\end{array}$

Accepted Answer

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

Question 12

Determine the solution to the system of equations graphically. If the system is inconsistent or dependent, so state.
-$$\begin{array} { l } 
y = - 9 x \
y = 9 x - 18
\end{array}$$

Accepted Answer

A) (1, 18) 
B) (-1, 9) 
C) (1, -9) 
D) dependent 
A) (1, 18) 
B) (-1, 9) 
C) (1, -9) 
D) dependent

Question 13

Solve the problem.
-Three solutions to the equation Ax + By + Cz = 14 are (5, -4, 1), (1, 3, 0), and (3, 1, -4). Determine the values of A, B, and C and write the equation using the numerical values found.

Accepted Answer

A) A = 3, B = 5, C = 1; 3x + 5y + z = 14 
B) A = 1, B = 3, C = 5; x + 3y + 5z = 14 
C) A = 5, B = 3, C = 1; 5x + 3y + z = 14 
D) A = 5, B = 1, C = 3; 5x + y + 3z = 14 
A) A = 3, B = 5, C = 1; 3x + 5y + z = 14 
B) A = 1, B = 3, C = 5; x + 3y + 5z = 14 
C) A = 5, B = 3, C = 1; 5x + 3y + z = 14 
D) A = 5, B = 1, C = 3; 5x + y + 3z = 14

Question 14

Write each equation in slope-intercept form. Without graphing the equations, state whether the system of equations is
consistent, inconsistent, or dependent. Also indicate whether the system has exactly one solution, no solution, or an
infinite number of solutions.
-$$\begin{array} { c } 
x + 3 y = 3 \
8 x - 5 y = - 5
\end{array}$$

Accepted Answer

A) inconsistent 
B) dependent 
C) consistent no solution infinite number of solutions one solution 
A) inconsistent 
B) dependent 
C) consistent no solution infinite number of solutions one solution

Question 15

Solve the system of equations using the addition method.
-$$\begin{array} { l } 
x - y + 2 z = 3 \
5 x + z = 0 \
x + 5 y + z = - 15
\end{array}$$

Accepted Answer

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

Question 16

Determine whether the system is inconsistent, dependent, or neither.
-$$\begin{array} { l } 
x - y + 2 z = - 2 \
4 x + z = 0 \
- x + y - 2 z = 4
\end{array}$$

Accepted Answer

A) dependent 
B) inconsistent 
C) neither 
A) dependent 
B) inconsistent 
C) neither

Question 17

Solve the problem.
-The Little Town Arts Center charges $22 for adults, $18 for senior citizens, and $7 for children under 12 for their live performances on Sunday afternoon. This past Sunday, the paid revenue was $11,615 for 755 tickets sold.
There were 44 more children than adults. How many children attended?

Accepted Answer

A) 257 children 
B) 285 children 
C) 213 children 
D) 247 children 
A) 257 children 
B) 285 children 
C) 213 children 
D) 247 children

Question 18

Determine the solution to the system of inequalities.
-$\begin{array} { l } 
y \geq 1 \
| x | > 5
\end{array}$

Accepted Answer

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

Question 19

Find the solution to the system of equations by substitution.
-$$\begin{array} { c } 
x + 6 y = - 45 \
- 6 x + 5 y = - 17
\end{array}$$

Accepted Answer

A) (3, -6) 
B) (-3, -7) 
C) (-4, -6) 
D) no solution 
A) (3, -6) 
B) (-3, -7) 
C) (-4, -6) 
D) no solution

Question 20

The figure shows the graphs of the cost and revenue functions for a company that manufactures and sells binoculars. Use
the information in the figure to answer the question.  
-The company's cost for manufacturing x binoculars is determined by the equation y = x + 1500. The revenue for selling x binoculars is determined by the equation y = 3x. The break-even point is the point at which the cost
And revenue equations intersect. How many binoculars must be produced and sold for the company to break
Even?

Accepted Answer

A) 750 binoculars 
B) 1500 binoculars 
C) 2700 binoculars 
D) 2250 binoculars 
A) 750 binoculars 
B) 1500 binoculars 
C) 2700 binoculars 
D) 2250 binoculars

Determine whether the ordered pair or ordered triple satisfies the system of linear equations. - y=-3x-7 y=-x- (-4,-5)

Solve the problem. -Jancie has $180,000 to invest to obtain annual income. She wants some of it invested in safe Certificates of Deposit yielding 7%. The rest she wants to invest in AA bonds yielding 11% per year. How much should she Invest in each to realize exactly $17,400 per year?

Determine the solution to the system of inequalities. - y<2x+2 y\leq-x $Determine the solution to the system of inequalities. - \begin{array} { l } y < 2 x + 2 \\ y \leq - \frac { 3 } { 2 } x \end{array}$

Evaluate the determinant. - $\left| \begin{array} { l l l } 1 & 2 & 5 \\2 & 4 & 3 \\1 & 2 & 5\end{array} \right|$

Solve the system of equations using the addition method. - -0.2x+0.3y-0.3z=-2.8 0.4x-0.1y+0.2z=2 -0.2x-0.4y+0.4z=2.8

Solve the system of equations using the addition method. - 5x+35y=35 9x-5y=-5

Determine the solution to the system of inequalities. - x\geq0 y\geq0 2x+2y\leq4 3x+y\leq5 $Determine the solution to the system of inequalities. - \begin{array} { l } x \geq 0 \\ y \geq 0 \\ 2 x + 2 y \leq 4 \\ 3 x + y \leq 5 \\ \end{array}$

Determine the solution to the system of equations graphically. If the system is inconsistent or dependent, so state. - y=-3x-1 -6x-2y=2

Solve the system of equations using determinants. - -4x-2y=-18 -8x=-20+4y

Determine the solution to the system of inequalities. - |y|>6 y\leqx-3 $Determine the solution to the system of inequalities. - \begin{array} { l } | y | > 6 \\ y \leq x - 3 \end{array}$

Determine the solution to the system of equations graphically. If the system is inconsistent or dependent, so state. - y=-9x y=9x-18

Solve the problem. -Three solutions to the equation Ax + By + Cz = 14 are (5, -4, 1), (1, 3, 0), and (3, 1, -4). Determine the values of A, B, and C and write the equation using the numerical values found.

Write each equation in slope-intercept form. Without graphing the equations, state whether the system of equations is consistent, inconsistent, or dependent. Also indicate whether the system has exactly one solution, no solution, or an infinite number of solutions. - x+3y=3 8x-5y=-5

Solve the system of equations using the addition method. - x-y+2z=3 5x+z=0 x+5y+z=-15

Determine whether the system is inconsistent, dependent, or neither. - x-y+2z=-2 4x+z=0 -x+y-2z=4

Determine the solution to the system of inequalities. - y\geq1 |x|>5 $Determine the solution to the system of inequalities. - \begin{array} { l } y \geq 1 \\ | x | > 5 \end{array}$

Find the solution to the system of equations by substitution. - x+6y=-45 -6x+5y=-17

Basic Concepts

Equations and Inequalities

Graphs and Functions

Polynomials and Polynomial Functions

Rational Expressions and Equations

Roots, Radicals, and Complex Numbers

Quadratic Functions

Exponential and Logarithmic Functions

Characteristics of Functions and Their Graphs

Conic Sections

Sequences, Series, and Probability

Filters

Exam 4: Systems of Equations and Inequalities

Determine whether the ordered pair or ordered triple satisfies the system of linear equations. - y=-3x-7 y=-x- (-4,-5)

Solve the problem. -Jancie has $180,000 to invest to obtain annual income. She wants some of it invested in safe Certificates of Deposit yielding 7%. The rest she wants to invest in AA bonds yielding 11% per year. How much should she Invest in each to realize exactly $17,400 per year?

Determine the solution to the system of inequalities. - y<2x+2 y\leq-x

Evaluate the determinant. - ∣125243125∣\left| \begin{array} { l l l } 1 & 2 & 5 \\2 & 4 & 3 \\1 & 2 & 5\end{array} \right|​121​242​535​​

Solve the system of equations using the addition method. - -0.2x+0.3y-0.3z=-2.8 0.4x-0.1y+0.2z=2 -0.2x-0.4y+0.4z=2.8

Solve the system of equations using the addition method. - 5x+35y=35 9x-5y=-5

Determine the solution to the system of inequalities. - x\geq0 y\geq0 2x+2y\leq4 3x+y\leq5

Determine the solution to the system of equations graphically. If the system is inconsistent or dependent, so state. - y=-3x-1 -6x-2y=2

Solve the system of equations using determinants. - -4x-2y=-18 -8x=-20+4y

Determine the solution to the system of inequalities. - |y|>6 y\leqx-3

Determine the solution to the system of equations graphically. If the system is inconsistent or dependent, so state. - y=-9x y=9x-18

Solve the problem. -Three solutions to the equation Ax + By + Cz = 14 are (5, -4, 1), (1, 3, 0), and (3, 1, -4). Determine the values of A, B, and C and write the equation using the numerical values found.

Write each equation in slope-intercept form. Without graphing the equations, state whether the system of equations is consistent, inconsistent, or dependent. Also indicate whether the system has exactly one solution, no solution, or an infinite number of solutions. - x+3y=3 8x-5y=-5

Solve the system of equations using the addition method. - x-y+2z=3 5x+z=0 x+5y+z=-15

Determine whether the system is inconsistent, dependent, or neither. - x-y+2z=-2 4x+z=0 -x+y-2z=4

Determine the solution to the system of inequalities. - y\geq1 |x|>5

Find the solution to the system of equations by substitution. - x+6y=-45 -6x+5y=-17

Basic Concepts

Equations and Inequalities

Graphs and Functions

Polynomials and Polynomial Functions

Rational Expressions and Equations

Roots, Radicals, and Complex Numbers

Quadratic Functions

Exponential and Logarithmic Functions

Characteristics of Functions and Their Graphs

Conic Sections

Sequences, Series, and Probability

Filters

Determine the solution to the system of inequalities. - y<2x+2 y\leq-x $Determine the solution to the system of inequalities. - \begin{array} { l } y < 2 x + 2 \\ y \leq - \frac { 3 } { 2 } x \end{array}$

Evaluate the determinant. - $\left| \begin{array} { l l l } 1 & 2 & 5 \\2 & 4 & 3 \\1 & 2 & 5\end{array} \right|$

Determine the solution to the system of inequalities. - x\geq0 y\geq0 2x+2y\leq4 3x+y\leq5 $Determine the solution to the system of inequalities. - \begin{array} { l } x \geq 0 \\ y \geq 0 \\ 2 x + 2 y \leq 4 \\ 3 x + y \leq 5 \\ \end{array}$

Determine the solution to the system of inequalities. - |y|>6 y\leqx-3 $Determine the solution to the system of inequalities. - \begin{array} { l } | y | > 6 \\ y \leq x - 3 \end{array}$

Determine the solution to the system of inequalities. - y\geq1 |x|>5 $Determine the solution to the system of inequalities. - \begin{array} { l } y \geq 1 \\ | x | > 5 \end{array}$