Question 1

Is the ordered triple a solution to the given system of equations?
-$(5,-4,5)$
$\begin{aligned}
& 2 x-3 y+3 z=24 \
& 4 x+4 y-3 z=-8 \
& 3 x-3 y+2 z=23
\end{aligned}$

Accepted Answer

A) True 
 B)False

Question 2

A chemist needs 100 milliliters of a $53 \%$ solution but has only $43 \%$ and $93 \%$ solutions available. Find how many milliliters of each that should be mixed to get the desired solution.

Accepted Answer

A)  $83 \mathrm{ml}$ of $43 \%$; $17 \mathrm{ml}$ of $93 \%$ 
B)  $83 \mathrm{ml}$ of $43 \% ; 20 \mathrm{ml}$ of $93 \%$ 
C)  $20 \mathrm{ml}$ of $43 \%$; $80 \mathrm{ml}$ of $93 \%$ 
D)  $80 \mathrm{ml}$ of $43 \% ; 20 \mathrm{ml}$ of $93 \%$ 
A)  $83 \mathrm{ml}$ of $43 \%$; $17 \mathrm{ml}$ of $93 \%$ 
B)  $83 \mathrm{ml}$ of $43 \% ; 20 \mathrm{ml}$ of $93 \%$ 
C)  $20 \mathrm{ml}$ of $43 \%$; $80 \mathrm{ml}$ of $93 \%$ 
D)  $80 \mathrm{ml}$ of $43 \% ; 20 \mathrm{ml}$ of $93 \%$

Question 3

Graph the system of inequalities.
-$\begin{aligned} & 6 y-x \leq 8 \ & -y+3 x \leq 6 \ & x \leq 0\end{aligned}$

Accepted Answer

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

Question 4

Solve by addition or substitution.
-$-4 x+2 y=3$
$4 \mathrm{x}-2 \mathrm{y}=3$

Accepted Answer

A)  $\left(0, \frac{3}{2}\right)$ 
B)  $\left(\frac{3}{4}, 0\right)$ 
C)  $\{(r, s) \mid-4 r+2 s=3\}$ 
D)  $\varnothing$ 
A)  $\left(0, \frac{3}{2}\right)$ 
B)  $\left(\frac{3}{4}, 0\right)$ 
C)  $\{(r, s) \mid-4 r+2 s=3\}$ 
D)  $\varnothing$

Question 5

Solve by addition or substitution.
-$x+9 y=59$
$2 \mathrm{x}+9 \mathrm{y}=64$

Accepted Answer

A)  $(-5,5)$ 
B)  $(5,6)$ 
C)  $(6,5)$ 
D)  $\varnothing$ 
A)  $(-5,5)$ 
B)  $(5,6)$ 
C)  $(6,5)$ 
D)  $\varnothing$

Question 6

Solve by addition or substitution.
-$3 y+x=9$
$\mathrm{x}=4 \mathrm{y}+2$

Accepted Answer

A)  $(-6,1)$ 
B)  $(6,-1)$ 
C)  $(6,1)$ 
D)  $(-6,-1)$ 
A)  $(-6,1)$ 
B)  $(6,-1)$ 
C)  $(6,1)$ 
D)  $(-6,-1)$

Question 7

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

Accepted Answer

A)  $(12,20)$ 
B)  $(6,10)$ 
C)  $(20,12)$ 
D)  $(10,6)$ 
A)  $(12,20)$ 
B)  $(6,10)$ 
C)  $(20,12)$ 
D)  $(10,6)$

Question 8

Solve the system of equations using Cramer's rule.
-$x-4 y-2 z=-29$
$-3 x+y+z=-6$
$-2 \mathrm{x}+4 \mathrm{y}-\mathrm{z}=21$

Accepted Answer

A)  $(5,1,8)$ 
B)  $(-5,8,10)$ 
C)  $(5,8,1)$ 
D)  $(8,1,5)$ 
A)  $(5,1,8)$ 
B)  $(-5,8,10)$ 
C)  $(5,8,1)$ 
D)  $(8,1,5)$

Question 9

The perimeter of a rectangle is $34 \mathrm{~cm}$. The length is $11 \mathrm{~cm}$ longer than the width. Find the dimensions.

Accepted Answer

A)  Width: $10 \mathrm{~cm}$; length: $21 \mathrm{~cm}$ 
B)  Width: $3 \mathrm{~cm}$; length: $11 \mathrm{~cm}$ 
C)  Width: $6 \mathrm{~cm}$; length: $17 \mathrm{~cm}$ 
D)  Width: $3 \mathrm{~cm}$; length: $14 \mathrm{~cm}$ 
A)  Width: $10 \mathrm{~cm}$; length: $21 \mathrm{~cm}$ 
B)  Width: $3 \mathrm{~cm}$; length: $11 \mathrm{~cm}$ 
C)  Width: $6 \mathrm{~cm}$; length: $17 \mathrm{~cm}$ 
D)  Width: $3 \mathrm{~cm}$; length: $14 \mathrm{~cm}$

Question 10

Solve the system of four equations in four unknowns using matrices.Solve the system of four equations in four unknowns using matrices.
-$\begin{aligned} \mathrm{x}+3 \mathrm{y}-2 \mathrm{z}-\mathrm{w} & =16 \ 4 \mathrm{x}+\mathrm{y}+\mathrm{z}+2 \mathrm{w} & =10 \ -3 \mathrm{x}-\mathrm{y}-3 \mathrm{z}-2 \mathrm{w} & =1 \ \mathrm{x}-\mathrm{y}-3 \mathrm{z}-2 \mathrm{w} & =5\end{aligned}$

Accepted Answer

A)  $(16,10,1,5)$ 
B)  $(-1,3,-5,6)$ 
C)  $(0,5,-9,6)$ 
D)  $(1,3,-5,4)$ 
A)  $(16,10,1,5)$ 
B)  $(-1,3,-5,6)$ 
C)  $(0,5,-9,6)$ 
D)  $(1,3,-5,4)$

Question 11

Graph the system of inequalities.
-$y \geq x + 1 $
$y \leq x + 7$
$2\leq x \leq 9$

Accepted Answer

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

Question 12

Graph the system of inequalities.
-$3 x+2 y \leq-6$
$x \geq 1$

Accepted Answer

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

Question 13

Solve by addition or substitution.
-$\frac{1}{5} x-\frac{1}{4} y=3$
$\frac{2}{5} x+\frac{1}{2} y=2$

Accepted Answer

A)  $(-10,-6)$ 
B)  $(10,-4)$ 
C)  $(20,-4)$ 
D)  $\varnothing$ 
A)  $(-10,-6)$ 
B)  $(10,-4)$ 
C)  $(20,-4)$ 
D)  $\varnothing$

Question 14

The perimeter of a rectangle is $78 \mathrm{~m}$. If the width were doubled and the length were increased by $25 \mathrm{~m}$, then the perimeter would be $158 \mathrm{~m}$. What are the dimensions?

Accepted Answer

A)  Width: $15 \mathrm{~m}$; length: $24 \mathrm{~m}$ 
B)  Width: $19 \mathrm{~m}$; length: $19 \mathrm{~m}$ 
C)  Width: $14 \mathrm{~m}$; length: $19 \mathrm{~m}$ 
D)  Width: $24 \mathrm{~m}$; length: $15 \mathrm{~m}$ 
A)  Width: $15 \mathrm{~m}$; length: $24 \mathrm{~m}$ 
B)  Width: $19 \mathrm{~m}$; length: $19 \mathrm{~m}$ 
C)  Width: $14 \mathrm{~m}$; length: $19 \mathrm{~m}$ 
D)  Width: $24 \mathrm{~m}$; length: $15 \mathrm{~m}$

Question 15

Michael's bank contains only nickels, dimes, and quarters. There are 64 coins in all, valued at $\$$ 5.40. The number of nickels is 4 short of being three times the sum of the number of dimes and quarters together. How many dimes are in the bank?

Accepted Answer

A)  8 
B)  9 
C)  13 
D)  47 
A)  8 
B)  9 
C)  13 
D)  47

Question 16

Solve the system of equations using Cramer's rule.
-$3 x+5 y=-33$
$6 x+7 y=-48$

Accepted Answer

A)  $(-2,-5)$ 
B)  $(-1,-6)$ 
C)  $(-1,6)$ 
D)  $(0,-7)$ 
A)  $(-2,-5)$ 
B)  $(-1,-6)$ 
C)  $(-1,6)$ 
D)  $(0,-7)$

Question 17

A contractor mixes concrete from bags of pre mix for small jobs. How many bags with $8 \%$ cement should he mix with 4 bags of $18 \%$ cement to produce a mix containing $10 \%$ cement?

Accepted Answer

A)  20 bags 
B)  25 bags 
C)  18 bags 
D)  16 bags 
A)  20 bags 
B)  25 bags 
C)  18 bags 
D)  16 bags

Question 18

Linda invests $\$ 25,000$ for one year. Part is invested at $5 \%$, another part at $6 \%$, and the rest at $8 \%$. The total income from all 3 investments is $\$ 1600$. The income from the $5 \%$ and $6 \%$ investments is the same as the income from the $8 \%$ investment. Find the amount invested at each rate.

Accepted Answer

A)  At $5 \%$ : $\$ 8000$; at $6 \%: \$ 10,000$; at $8 \%: \$ 7000$ 
B)  At $5 \%$ : $\$ 5000$; at $6 \%: \$ 10,000$; at $8 \%: \$ 10,000$ 
C)  At $5 \%$ : $\$ 10,000$; at $6 \%$ : $\$ 5000$; at $8 \%$ : $\$ 10,000$ 
D)  At 5\%: $\$ 10,000$; at $6 \%$ : $\$ 10,000$; at $8 \%$ : $\$ 5000$ 
A)  At $5 \%$ : $\$ 8000$; at $6 \%: \$ 10,000$; at $8 \%: \$ 7000$ 
B)  At $5 \%$ : $\$ 5000$; at $6 \%: \$ 10,000$; at $8 \%: \$ 10,000$ 
C)  At $5 \%$ : $\$ 10,000$; at $6 \%$ : $\$ 5000$; at $8 \%$ : $\$ 10,000$ 
D)  At 5\%: $\$ 10,000$; at $6 \%$ : $\$ 10,000$; at $8 \%$ : $\$ 5000$

Question 19

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 $x$.
-$\frac{7}{3} x+\frac{5}{4} y=4$
$\frac{5}{6} x-2 y=21$

Accepted Answer

A)  $\varnothing$ 
B)  $(6,-8)$ 
C)  $(-6,8)$ 
D)  $\left(x,-\frac{5}{12} x-\frac{21}{2}\right)$ 
A)  $\varnothing$ 
B)  $(6,-8)$ 
C)  $(-6,8)$ 
D)  $\left(x,-\frac{5}{12} x-\frac{21}{2}\right)$

Question 20

Solve the system by graphing. 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 $x$.
-$x=2$
$y=4$

Accepted Answer

A)  $(4,2)$ 
B)  Inconsistent, $\varnothing$ 
C)  $(2,4)$ 
D)  $(2,2)$ 
A)  $(4,2)$ 
B)  Inconsistent, $\varnothing$ 
C)  $(2,4)$ 
D)  $(2,2)$

Is the ordered triple a solution to the given system of equations? - $(5,-4,5)$ 2x-3y+3z=24 4x+4y-3z=-8 3x-3y+2z=23

A chemist needs 100 milliliters of a $53 \%$ solution but has only $43 \%$ and $93 \%$ solutions available. Find how many milliliters of each that should be mixed to get the desired solution.

Graph the system of inequalities. - 6y-x\leq8 -y+3x\leq6 x\leq0 $Graph the system of inequalities. - \begin{aligned} & 6 y-x \leq 8 \\ & -y+3 x \leq 6 \\ & x \leq 0\end{aligned}$

Solve by addition or substitution. - $-4 x+2 y=3$ $4 \mathrm{x}-2 \mathrm{y}=3$

Solve by addition or substitution. - $x+9 y=59$ $2 \mathrm{x}+9 \mathrm{y}=64$

Solve by addition or substitution. - $3 y+x=9$ $\mathrm{x}=4 \mathrm{y}+2$

Solve the system of equations using Cramer's rule. - $x-4 y-2 z=-29$ $-3 x+y+z=-6$ $-2 \mathrm{x}+4 \mathrm{y}-\mathrm{z}=21$

The perimeter of a rectangle is $34 \mathrm{~cm}$ . The length is $11 \mathrm{~cm}$ longer than the width. Find the dimensions.

Solve the system of four equations in four unknowns using matrices.Solve the system of four equations in four unknowns using matrices. - +3-2- =16 4+++2 =10 -3--3-2 =1 --3-2 =5

Graph the system of inequalities. - $y \geq x + 1$ $y \leq x + 7$ $2\leq x \leq 9$ $Graph the system of inequalities. - y \geq x + 1 y \leq x + 7 2\leq x \leq 9$

Graph the system of inequalities. - $3 x+2 y \leq-6$ $x \geq 1$ $Graph the system of inequalities. - 3 x+2 y \leq-6 x \geq 1$

Solve by addition or substitution. - $\frac{1}{5} x-\frac{1}{4} y=3$ $\frac{2}{5} x+\frac{1}{2} y=2$

The perimeter of a rectangle is $78 \mathrm{~m}$ . If the width were doubled and the length were increased by $25 \mathrm{~m}$ , then the perimeter would be $158 \mathrm{~m}$ . What are the dimensions?

Michael's bank contains only nickels, dimes, and quarters. There are 64 coins in all, valued at $\$$ 5.40. The number of nickels is 4 short of being three times the sum of the number of dimes and quarters together. How many dimes are in the bank?

Solve the system of equations using Cramer's rule. - $3 x+5 y=-33$ $6 x+7 y=-48$

A contractor mixes concrete from bags of pre mix for small jobs. How many bags with $8 \%$ cement should he mix with 4 bags of $18 \%$ cement to produce a mix containing $10 \%$ cement?

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 $x$ . - $\frac{7}{3} x+\frac{5}{4} y=4$ $\frac{5}{6} x-2 y=21$

Solve the system by graphing. 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 $x$ . - $x=2$ $y=4$

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

Is the ordered triple a solution to the given system of equations? - (5,−4,5)(5,-4,5)(5,−4,5) 2x-3y+3z=24 4x+4y-3z=-8 3x-3y+2z=23

A chemist needs 100 milliliters of a 53%53 \%53% solution but has only 43%43 \%43% and 93%93 \%93% solutions available. Find how many milliliters of each that should be mixed to get the desired solution.

Graph the system of inequalities. - 6y-x\leq8 -y+3x\leq6 x\leq0

Solve by addition or substitution. - −4x+2y=3-4 x+2 y=3−4x+2y=3 4x−2y=34 \mathrm{x}-2 \mathrm{y}=34x−2y=3

Solve by addition or substitution. - x+9y=59x+9 y=59x+9y=59 2x+9y=642 \mathrm{x}+9 \mathrm{y}=642x+9y=64

Solve by addition or substitution. - 3y+x=93 y+x=93y+x=9 x=4y+2\mathrm{x}=4 \mathrm{y}+2x=4y+2

Solve the system by graphing. 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 . - y =x-4 y =-x+16

Solve the system of equations using Cramer's rule. - x−4y−2z=−29x-4 y-2 z=-29x−4y−2z=−29 −3x+y+z=−6-3 x+y+z=-6−3x+y+z=−6 −2x+4y−z=21-2 \mathrm{x}+4 \mathrm{y}-\mathrm{z}=21−2x+4y−z=21

The perimeter of a rectangle is 34 cm34 \mathrm{~cm}34 cm . The length is 11 cm11 \mathrm{~cm}11 cm longer than the width. Find the dimensions.

Solve the system of four equations in four unknowns using matrices.Solve the system of four equations in four unknowns using matrices. - +3-2- =16 4+++2 =10 -3--3-2 =1 --3-2 =5

Graph the system of inequalities. - y≥x+1y \geq x + 1 y≥x+1 y≤x+7y \leq x + 7y≤x+7 2≤x≤92\leq x \leq 92≤x≤9

Graph the system of inequalities. - 3x+2y≤−63 x+2 y \leq-63x+2y≤−6 x≥1x \geq 1x≥1

Solve by addition or substitution. - 15x−14y=3\frac{1}{5} x-\frac{1}{4} y=351​x−41​y=3 25x+12y=2\frac{2}{5} x+\frac{1}{2} y=252​x+21​y=2

The perimeter of a rectangle is 78 m78 \mathrm{~m}78 m . If the width were doubled and the length were increased by 25 m25 \mathrm{~m}25 m , then the perimeter would be 158 m158 \mathrm{~m}158 m . What are the dimensions?

Michael's bank contains only nickels, dimes, and quarters. There are 64 coins in all, valued at $\$$ 5.40. The number of nickels is 4 short of being three times the sum of the number of dimes and quarters together. How many dimes are in the bank?

Solve the system of equations using Cramer's rule. - 3x+5y=−333 x+5 y=-333x+5y=−33 6x+7y=−486 x+7 y=-486x+7y=−48

A contractor mixes concrete from bags of pre mix for small jobs. How many bags with 8%8 \%8% cement should he mix with 4 bags of 18%18 \%18% cement to produce a mix containing 10%10 \%10% cement?

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 . - 73x+54y=4\frac{7}{3} x+\frac{5}{4} y=437​x+45​y=4 56x−2y=21\frac{5}{6} x-2 y=2165​x−2y=21

Solve the system by graphing. 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=2x=2x=2 y=4y=4y=4

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

Is the ordered triple a solution to the given system of equations? - $(5,-4,5)$ 2x-3y+3z=24 4x+4y-3z=-8 3x-3y+2z=23

A chemist needs 100 milliliters of a $53 \%$ solution but has only $43 \%$ and $93 \%$ solutions available. Find how many milliliters of each that should be mixed to get the desired solution.

Graph the system of inequalities. - 6y-x\leq8 -y+3x\leq6 x\leq0 $Graph the system of inequalities. - \begin{aligned} & 6 y-x \leq 8 \\ & -y+3 x \leq 6 \\ & x \leq 0\end{aligned}$

Solve by addition or substitution. - $-4 x+2 y=3$ $4 \mathrm{x}-2 \mathrm{y}=3$

Solve by addition or substitution. - $x+9 y=59$ $2 \mathrm{x}+9 \mathrm{y}=64$

Solve by addition or substitution. - $3 y+x=9$ $\mathrm{x}=4 \mathrm{y}+2$

Solve the system of equations using Cramer's rule. - $x-4 y-2 z=-29$ $-3 x+y+z=-6$ $-2 \mathrm{x}+4 \mathrm{y}-\mathrm{z}=21$

The perimeter of a rectangle is $34 \mathrm{~cm}$ . The length is $11 \mathrm{~cm}$ longer than the width. Find the dimensions.

Graph the system of inequalities. - $y \geq x + 1$ $y \leq x + 7$ $2\leq x \leq 9$ $Graph the system of inequalities. - y \geq x + 1 y \leq x + 7 2\leq x \leq 9$

Graph the system of inequalities. - $3 x+2 y \leq-6$ $x \geq 1$ $Graph the system of inequalities. - 3 x+2 y \leq-6 x \geq 1$

Solve by addition or substitution. - $\frac{1}{5} x-\frac{1}{4} y=3$ $\frac{2}{5} x+\frac{1}{2} y=2$

The perimeter of a rectangle is $78 \mathrm{~m}$ . If the width were doubled and the length were increased by $25 \mathrm{~m}$ , then the perimeter would be $158 \mathrm{~m}$ . What are the dimensions?

Solve the system of equations using Cramer's rule. - $3 x+5 y=-33$ $6 x+7 y=-48$

A contractor mixes concrete from bags of pre mix for small jobs. How many bags with $8 \%$ cement should he mix with 4 bags of $18 \%$ cement to produce a mix containing $10 \%$ cement?

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 $x$ . - $\frac{7}{3} x+\frac{5}{4} y=4$ $\frac{5}{6} x-2 y=21$

Solve the system by graphing. 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 $x$ . - $x=2$ $y=4$