Question 1

Solve the system of equations using Cramer's rule.
-$x-y+z=-11$
$x+y+z=-3$
$\mathrm{x}+\mathrm{y}-\mathrm{z}=1$

Accepted Answer

A)  $(-5,-2,4)$ 
B)  $(-5,4,-2)$ 
C)  $(4,-2,-5)$ 
D)  $(-2,-5,4)$ 
A)  $(-5,-2,4)$ 
B)  $(-5,4,-2)$ 
C)  $(4,-2,-5)$ 
D)  $(-2,-5,4)$

Question 2

Solve the system using the addition method. If the system is inconsistent and has no solution, state this. If the system is dependent, write the form of the solution for any real number $x$.
-$2 x-7 y=6$
$4 x-14 y=30$

Accepted Answer

A)  $(6,30)$ 
B)  $\left(6,-\frac{12}{7}\right)$ 
C)  $(2,5)$ 
D)  $\varnothing$ 
A)  $(6,30)$ 
B)  $\left(6,-\frac{12}{7}\right)$ 
C)  $(2,5)$ 
D)  $\varnothing$

Question 3

Solve the system of four equations in four unknowns using matrices.
-$-\mathrm{w}+\mathrm{x}+\mathrm{y}+\mathrm{z}=7$
$\mathrm{w}+\mathrm{x}+\mathrm{y}-\mathrm{z}=3$
$\mathrm{w}+2 \mathrm{x}+3 \mathrm{y}+\mathrm{z}=19$
$3 \mathrm{w}-\mathrm{x}+\mathrm{y}+2 \mathrm{z}=16$

Accepted Answer

A)  $(1,4,5,3)$ 
B)  $(3,4,1,5)$ 
C)  $(4,1,3,5)$ 
D)  $(0,4,0,1)$ 
A)  $(1,4,5,3)$ 
B)  $(3,4,1,5)$ 
C)  $(4,1,3,5)$ 
D)  $(0,4,0,1)$

Question 4

Solve the system of equations using Cramer's rule.
-$\begin{array}{l}
\mathrm{x} \quad+\mathrm{y} \quad+\mathrm{z}=10,000 \
x \quad-z=-500 \
\end{array}$
 $0.03 x+0.05 y-0.07 z=20$

Accepted Answer

A)  $(3000,3000,4000)$ 
B)  $(2500,4000,3500)$ 
C)  $(3500,3500,4000)$ 
D)  $(3000,3500,3500)$ 
A)  $(3000,3000,4000)$ 
B)  $(2500,4000,3500)$ 
C)  $(3500,3500,4000)$ 
D)  $(3000,3500,3500)$

Question 5

A boat travels 12 miles downstream in 4 hours and returns upstream in 6 hours. Find the speed of the current and the speed of the boat in still water.

Accepted Answer

A)  Boat: $2.5 \mathrm{mph}$; current: $0.5 \mathrm{mph}$ 
B)  Boat: $0.5 \mathrm{mph}$; current: $2.5 \mathrm{mph}$ 
C)  Boat: $5.5 \mathrm{mph}$; current: $3 \mathrm{mph}$ 
D)  Boat: $3 \mathrm{mph}$; current: $0.5 \mathrm{mph}$ 
A)  Boat: $2.5 \mathrm{mph}$; current: $0.5 \mathrm{mph}$ 
B)  Boat: $0.5 \mathrm{mph}$; current: $2.5 \mathrm{mph}$ 
C)  Boat: $5.5 \mathrm{mph}$; current: $3 \mathrm{mph}$ 
D)  Boat: $3 \mathrm{mph}$; current: $0.5 \mathrm{mph}$

Question 6

Anne and Nancy use a metal alloy that is $17.4 \%$ copper to make jewelry. How many ounces of an alloy that is $13 \%$ copper must be mixed with an alloy that is $24 \%$ copper to form 85 ounces of the desired alloy?

Accepted Answer

A)  $39 \mathrm{oz}$ 
B)  $51 \mathrm{oz}$ 
C)  $53 \mathrm{oz}$ 
D)  $34 \mathrm{oz}$ 
A)  $39 \mathrm{oz}$ 
B)  $51 \mathrm{oz}$ 
C)  $53 \mathrm{oz}$ 
D)  $34 \mathrm{oz}$

Question 7

Solve the system by substitution. If the system is inconsistent and has no solution, state this. If the system is dependent, write the form of the solution for any real number $x$.
-$5 y+x=-5$
$\mathrm{x}=2 \mathrm{y}-6$

Accepted Answer

A)  $\left(-\frac{40}{7},-\frac{1}{7}\right)$ 
B)  $\left(\frac{40}{7},-\frac{1}{7}\right)$ 
C)  $\left(\frac{40}{7}, \frac{1}{7}\right)$ 
D)  $\left(-\frac{40}{7}, \frac{1}{7}\right)$ 
A)  $\left(-\frac{40}{7},-\frac{1}{7}\right)$ 
B)  $\left(\frac{40}{7},-\frac{1}{7}\right)$ 
C)  $\left(\frac{40}{7}, \frac{1}{7}\right)$ 
D)  $\left(-\frac{40}{7}, \frac{1}{7}\right)$

Question 8

Two angles have a sum of $78^{\circ}$. Their difference is $2^{\circ}$. Find the angles.

Accepted Answer

A)  $40^{\circ}$ and $38^{\circ}$ 
B)  $77^{\circ}$ and $1^{\circ}$ 
C)  $38^{\circ}$ and $40^{\circ}$ 
D)  $40^{\circ}$ and $42^{\circ}$ 
A)  $40^{\circ}$ and $38^{\circ}$ 
B)  $77^{\circ}$ and $1^{\circ}$ 
C)  $38^{\circ}$ and $40^{\circ}$ 
D)  $40^{\circ}$ and $42^{\circ}$

Question 9

A sum of money amounting to $\$ 3.75$ consists of dimes and quarters. If there are 27 coins in all, how many are quarters?

Accepted Answer

A)  22 quarters 
B)  12 quarters 
C)  20 quarters 
D)  7 quarters 
A)  22 quarters 
B)  12 quarters 
C)  20 quarters 
D)  7 quarters

Question 10

Solve the system using the addition method. If the system is inconsistent and has no solution, state this. If the system is dependent, write the form of the solution for any real number $x$.
-$x+y=9$
$\mathrm{x}+\mathrm{y}=-1$

Accepted Answer

A)  $(9,-1)$ 
B)  $(0,8)$ 
C)  $(x, 8-x)$ 
D)  $\varnothing$ 
A)  $(9,-1)$ 
B)  $(0,8)$ 
C)  $(x, 8-x)$ 
D)  $\varnothing$

Question 11

Solve the system of equations using matrices.
-$-x+5 y=-6$
$5 x-3 y=-14$

Accepted Answer

A)  $(1,-1)$ 
B)  $(-9,-3)$ 
C)  $(6,0)$ 
D)  $(-4,-2)$ 
A)  $(1,-1)$ 
B)  $(-9,-3)$ 
C)  $(6,0)$ 
D)  $(-4,-2)$

Question 12

Graph the system of inequalities.
-$\begin{array}{l}
3 y+x \geq 0 \
y+2 x \leq 10 \
y \geq 0
\end{array}$

Accepted Answer

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

Question 13

Jarod is having a problem with rabbits getting into his vegetable garden, so he decides to fence it in. The length of the garden is 8 feet more than 5 times the width. He needs 100 feet of fencing to do the job. Find the dimensions of the garden.

Accepted Answer

A)  length: $84 \frac{2}{3} \mathrm{ft}$; width: $15 \frac{1}{3} \mathrm{ft}$ 
B)  length: $38 \mathrm{ft}$; width: $6 \mathrm{ft}$ 
C)  length: $48 \mathrm{ft}$; width: $8 \mathrm{ft}$ 
D)  length: $43 \mathrm{ft}$; width: $7 \mathrm{ft}$ 
A)  length: $84 \frac{2}{3} \mathrm{ft}$; width: $15 \frac{1}{3} \mathrm{ft}$ 
B)  length: $38 \mathrm{ft}$; width: $6 \mathrm{ft}$ 
C)  length: $48 \mathrm{ft}$; width: $8 \mathrm{ft}$ 
D)  length: $43 \mathrm{ft}$; width: $7 \mathrm{ft}$

Question 14

Draw the graph of a linear equation that, along with the given line, forms a system whose single solution is the ordered pair $(0,1)$.

Accepted Answer

Answers may vary. Th

Question 15

Graph the system of inequalities.
-$x \geq-5$
$x<3$
$y \geq \frac{1}{4} x+2$

Accepted Answer

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

Question 16

Maria invested a total of $\$ 27,000$ in three different mutual funds. After one year, the first fund had shown a loss of $4 \%$, the second had shown a profit of $8 \%$, and the third fund had shown a profit of $11 \%$. In the first year Maria made a profit of $\$ 1710$ from the three funds. If Maria invested twice as much in the fund that made a profit of $8 \%$ as she did in the fund that lost $4 \%$, how much did she initially invest in each fund?

Accepted Answer

A)  $\$ 7000$ at a loss of $4 \%, \$ 14,000$ at a profit of $8 \%, \$ 6000$ at a profit of $11 \%$ 
B)  $\$ 12,000$ at a loss of $4 \%, \$ 6000$ at a profit of $8 \%, \$ 9000$ at a profit of $11 \%$ 
C)  $\$ 5000$ at a loss of $4 \%, \$ 10,000$ at a profit of $8 \%, \$ 12,000$ at a profit of $11 \%$ 
D)  $\$ 6000$ at a loss of $4 \%, \$ 12,000$ at a profit of $8 \%, \$ 9000$ at a profit of $11 \%$ 
A)  $\$ 7000$ at a loss of $4 \%, \$ 14,000$ at a profit of $8 \%, \$ 6000$ at a profit of $11 \%$ 
B)  $\$ 12,000$ at a loss of $4 \%, \$ 6000$ at a profit of $8 \%, \$ 9000$ at a profit of $11 \%$ 
C)  $\$ 5000$ at a loss of $4 \%, \$ 10,000$ at a profit of $8 \%, \$ 12,000$ at a profit of $11 \%$ 
D)  $\$ 6000$ at a loss of $4 \%, \$ 12,000$ at a profit of $8 \%, \$ 9000$ at a profit of $11 \%$

Question 17

Solve the system of equations using Cramer's rule.
-$-\frac{2}{3} x+5 y-2 z=9$
$3 x+\frac{4}{3} y+z=-1$
$\mathrm{x}-3 \mathrm{y}+3 \mathrm{z}=0$

Accepted Answer

A)  $(-3,0,5)$ 
B)  $(-3,3,4)$ 
C)  $(0,3,5)$ 
D)  $(0,0,4)$ 
A)  $(-3,0,5)$ 
B)  $(-3,3,4)$ 
C)  $(0,3,5)$ 
D)  $(0,0,4)$

Question 18

Solve the system of equations using matrices.
-$x+y-z=-5$
$4 x+3 y-5 z=-12$
$3 \mathrm{x}-\mathrm{y}+4 \mathrm{z}=-16$

Accepted Answer

A)  $(-5,-3,-3)$ 
B)  $(-3,-4,-2)$ 
C)  $(-2,-5,-2)$ 
D)  $(-3,-5,-3)$ 
A)  $(-5,-3,-3)$ 
B)  $(-3,-4,-2)$ 
C)  $(-2,-5,-2)$ 
D)  $(-3,-5,-3)$

Question 19

Solve the system of equations using matrices.
-$x+9 y-8 z=60$
$9 x+y+z=53$
$9 \mathrm{x}-5 \mathrm{y}-\mathrm{z}=9$

Accepted Answer

A)  $(5,1,7)$ 
B)  $(7,1,5)$ 
C)  $(5,7,1)$ 
D)  $(-5,7,10)$ 
A)  $(5,1,7)$ 
B)  $(7,1,5)$ 
C)  $(5,7,1)$ 
D)  $(-5,7,10)$

Question 20

A basketball fieldhouse seats 15,000 . Courtside seats sell for $\$ 8$, endzone for $\$ 6$, and balcony for $\$$ 4. The total revenue from a sell- out is $\$ 76,000$. If half the courtside and balcony seats and all the endzone seats are sold, the total revenue is $\$ 44,000$. How many of each type are there?

Accepted Answer

A)  4000 courtside; 3000 endzone; 8000 balcony 
B)  3200 courtside; 1800 endzone; 10,000 balcony 
C)  3000 courtside; 3000 endzone; 8,000 balcony 
D)  3000 courtside; 2000 endzone; 10,000 balcony 
A)  4000 courtside; 3000 endzone; 8000 balcony 
B)  3200 courtside; 1800 endzone; 10,000 balcony 
C)  3000 courtside; 3000 endzone; 8,000 balcony 
D)  3000 courtside; 2000 endzone; 10,000 balcony

Solve the system of equations using Cramer's rule. - $x-y+z=-11$ $x+y+z=-3$ $\mathrm{x}+\mathrm{y}-\mathrm{z}=1$

Solve the system using the addition method. If the system is inconsistent and has no solution, state this. If the system is dependent, write the form of the solution for any real number $x$ . - $2 x-7 y=6$ $4 x-14 y=30$

Solve the system of four equations in four unknowns using matrices. - $-\mathrm{w}+\mathrm{x}+\mathrm{y}+\mathrm{z}=7$ $\mathrm{w}+\mathrm{x}+\mathrm{y}-\mathrm{z}=3$ $\mathrm{w}+2 \mathrm{x}+3 \mathrm{y}+\mathrm{z}=19$ $3 \mathrm{w}-\mathrm{x}+\mathrm{y}+2 \mathrm{z}=16$

Solve the system of equations using Cramer's rule. - ++=10,000 x-z=-500 $0.03 x+0.05 y-0.07 z=20$

A boat travels 12 miles downstream in 4 hours and returns upstream in 6 hours. Find the speed of the current and the speed of the boat in still water.

Anne and Nancy use a metal alloy that is $17.4 \%$ copper to make jewelry. How many ounces of an alloy that is $13 \%$ copper must be mixed with an alloy that is $24 \%$ copper to form 85 ounces of the desired alloy?

Solve the system by substitution. If the system is inconsistent and has no solution, state this. If the system is dependent, write the form of the solution for any real number $x$ . - $5 y+x=-5$ $\mathrm{x}=2 \mathrm{y}-6$

Two angles have a sum of $78^{\circ}$ . Their difference is $2^{\circ}$ . Find the angles.

A sum of money amounting to $\$ 3.75$ consists of dimes and quarters. If there are 27 coins in all, how many are quarters?

Solve the system using the addition method. If the system is inconsistent and has no solution, state this. If the system is dependent, write the form of the solution for any real number $x$ . - $x+y=9$ $\mathrm{x}+\mathrm{y}=-1$

Solve the system of equations using matrices. - $-x+5 y=-6$ $5 x-3 y=-14$

Graph the system of inequalities. - 3y+x\geq0 y+2x\leq10 y\geq0 $Graph the system of inequalities. - \begin{array}{l} 3 y+x \geq 0 \\ y+2 x \leq 10 \\ y \geq 0 \end{array}$

Jarod is having a problem with rabbits getting into his vegetable garden, so he decides to fence it in. The length of the garden is 8 feet more than 5 times the width. He needs 100 feet of fencing to do the job. Find the dimensions of the garden.

Draw the graph of a linear equation that, along with the given line, forms a system whose single solution is the ordered pair $(0,1)$ .

Graph the system of inequalities. - $x \geq-5$ $x<3$ $y \geq \frac{1}{4} x+2$ $Graph the system of inequalities. - x \geq-5 x<3 y \geq \frac{1}{4} x+2$

Solve the system of equations using Cramer's rule. - $-\frac{2}{3} x+5 y-2 z=9$ $3 x+\frac{4}{3} y+z=-1$ $\mathrm{x}-3 \mathrm{y}+3 \mathrm{z}=0$

Solve the system of equations using matrices. - $x+y-z=-5$ $4 x+3 y-5 z=-12$ $3 \mathrm{x}-\mathrm{y}+4 \mathrm{z}=-16$

Solve the system of equations using matrices. - $x+9 y-8 z=60$ $9 x+y+z=53$ $9 \mathrm{x}-5 \mathrm{y}-\mathrm{z}=9$

Review of Real Numbers

Linear and Absolute Value Equations and Inequalities

Graphing Linear Equations

Exponents, Polynomials, and Factoring Polynomials

Rational Expressions and Equations

Radical Expressions and Equations

Quadratic Equations

Logarithmic and Exponential Functions

Conic Sections

Sequences, Series, and the Binomial Theorem

Filters

Exam 4: Systems of Equations

Solve the system of equations using Cramer's rule. - x−y+z=−11x-y+z=-11x−y+z=−11 x+y+z=−3x+y+z=-3x+y+z=−3 x+y−z=1\mathrm{x}+\mathrm{y}-\mathrm{z}=1x+y−z=1

Solve the system using the addition method. If the system is inconsistent and has no solution, state this. If the system is dependent, write the form of the solution for any real number xxx . - 2x−7y=62 x-7 y=62x−7y=6 4x−14y=304 x-14 y=304x−14y=30

Solve the system of equations using Cramer's rule. - ++=10,000 x-z=-500 0.03x+0.05y−0.07z=200.03 x+0.05 y-0.07 z=200.03x+0.05y−0.07z=20

A boat travels 12 miles downstream in 4 hours and returns upstream in 6 hours. Find the speed of the current and the speed of the boat in still water.

Anne and Nancy use a metal alloy that is 17.4%17.4 \%17.4% copper to make jewelry. How many ounces of an alloy that is 13%13 \%13% copper must be mixed with an alloy that is 24%24 \%24% copper to form 85 ounces of the desired alloy?

Solve the system by substitution. If the system is inconsistent and has no solution, state this. If the system is dependent, write the form of the solution for any real number xxx . - 5y+x=−55 y+x=-55y+x=−5 x=2y−6\mathrm{x}=2 \mathrm{y}-6x=2y−6

Two angles have a sum of 78∘78^{\circ}78∘ . Their difference is 2∘2^{\circ}2∘ . Find the angles.

A sum of money amounting to $3.75\$ 3.75$3.75 consists of dimes and quarters. If there are 27 coins in all, how many are quarters?

Solve the system using the addition method. If the system is inconsistent and has no solution, state this. If the system is dependent, write the form of the solution for any real number xxx . - x+y=9x+y=9x+y=9 x+y=−1\mathrm{x}+\mathrm{y}=-1x+y=−1

Solve the system of equations using matrices. - −x+5y=−6-x+5 y=-6−x+5y=−6 5x−3y=−145 x-3 y=-145x−3y=−14

Graph the system of inequalities. - 3y+x\geq0 y+2x\leq10 y\geq0

Jarod is having a problem with rabbits getting into his vegetable garden, so he decides to fence it in. The length of the garden is 8 feet more than 5 times the width. He needs 100 feet of fencing to do the job. Find the dimensions of the garden.

Draw the graph of a linear equation that, along with the given line, forms a system whose single solution is the ordered pair (0,1)(0,1)(0,1) .

Graph the system of inequalities. - x≥−5x \geq-5x≥−5 x<3x<3x<3 y≥14x+2y \geq \frac{1}{4} x+2y≥41​x+2

Solve the system of equations using Cramer's rule. - −23x+5y−2z=9-\frac{2}{3} x+5 y-2 z=9−32​x+5y−2z=9 3x+43y+z=−13 x+\frac{4}{3} y+z=-13x+34​y+z=−1 x−3y+3z=0\mathrm{x}-3 \mathrm{y}+3 \mathrm{z}=0x−3y+3z=0

Solve the system of equations using matrices. - x+y−z=−5x+y-z=-5x+y−z=−5 4x+3y−5z=−124 x+3 y-5 z=-124x+3y−5z=−12 3x−y+4z=−163 \mathrm{x}-\mathrm{y}+4 \mathrm{z}=-163x−y+4z=−16

Solve the system of equations using matrices. - x+9y−8z=60x+9 y-8 z=60x+9y−8z=60 9x+y+z=539 x+y+z=539x+y+z=53 9x−5y−z=99 \mathrm{x}-5 \mathrm{y}-\mathrm{z}=99x−5y−z=9

Review of Real Numbers

Linear and Absolute Value Equations and Inequalities

Graphing Linear Equations

Exponents, Polynomials, and Factoring Polynomials

Rational Expressions and Equations

Radical Expressions and Equations

Quadratic Equations

Logarithmic and Exponential Functions

Conic Sections

Sequences, Series, and the Binomial Theorem

Filters

Solve the system of equations using Cramer's rule. - $x-y+z=-11$ $x+y+z=-3$ $\mathrm{x}+\mathrm{y}-\mathrm{z}=1$

Solve the system using the addition method. If the system is inconsistent and has no solution, state this. If the system is dependent, write the form of the solution for any real number $x$ . - $2 x-7 y=6$ $4 x-14 y=30$

Solve the system of equations using Cramer's rule. - ++=10,000 x-z=-500 $0.03 x+0.05 y-0.07 z=20$

Anne and Nancy use a metal alloy that is $17.4 \%$ copper to make jewelry. How many ounces of an alloy that is $13 \%$ copper must be mixed with an alloy that is $24 \%$ copper to form 85 ounces of the desired alloy?

Solve the system by substitution. If the system is inconsistent and has no solution, state this. If the system is dependent, write the form of the solution for any real number $x$ . - $5 y+x=-5$ $\mathrm{x}=2 \mathrm{y}-6$

Two angles have a sum of $78^{\circ}$ . Their difference is $2^{\circ}$ . Find the angles.

A sum of money amounting to $\$ 3.75$ consists of dimes and quarters. If there are 27 coins in all, how many are quarters?

Solve the system using the addition method. If the system is inconsistent and has no solution, state this. If the system is dependent, write the form of the solution for any real number $x$ . - $x+y=9$ $\mathrm{x}+\mathrm{y}=-1$

Solve the system of equations using matrices. - $-x+5 y=-6$ $5 x-3 y=-14$

Graph the system of inequalities. - 3y+x\geq0 y+2x\leq10 y\geq0 $Graph the system of inequalities. - \begin{array}{l} 3 y+x \geq 0 \\ y+2 x \leq 10 \\ y \geq 0 \end{array}$

Draw the graph of a linear equation that, along with the given line, forms a system whose single solution is the ordered pair $(0,1)$ .

Graph the system of inequalities. - $x \geq-5$ $x<3$ $y \geq \frac{1}{4} x+2$ $Graph the system of inequalities. - x \geq-5 x<3 y \geq \frac{1}{4} x+2$

Solve the system of equations using Cramer's rule. - $-\frac{2}{3} x+5 y-2 z=9$ $3 x+\frac{4}{3} y+z=-1$ $\mathrm{x}-3 \mathrm{y}+3 \mathrm{z}=0$

Solve the system of equations using matrices. - $x+y-z=-5$ $4 x+3 y-5 z=-12$ $3 \mathrm{x}-\mathrm{y}+4 \mathrm{z}=-16$

Solve the system of equations using matrices. - $x+9 y-8 z=60$ $9 x+y+z=53$ $9 \mathrm{x}-5 \mathrm{y}-\mathrm{z}=9$