Question 1

Is the ordered pair a solution of the given system of equations?
-$(-6,-6), \begin{aligned} & 2 x+y=-6 \ & 3 x+2 y=-6\end{aligned}$

Accepted Answer

A) True 
 B)False

Question 2

Dmitri needs 6 liters of a $14 \%$ solution of sulfuric acid for a research project in molecular biology. He has two supplies of sulfuric acid solution: one is an unlimited supply of the $18 \%$ solution and the other an unlimited supply of the $12 \%$ solution. How many liters of each solution should Dmitri use?

Accepted Answer

A)  $4 \mathrm{~L}$ of $18 \%$ solution; $2 \mathrm{~L}$ of $12 \%$ solution 
B)  $2.5 \mathrm{~L}$ of $18 \%$ solution; $3.5 \mathrm{~L}$ of $12 \%$ solution 
C)  $2 \mathrm{~L}$ of $18 \%$ solution; $4 \mathrm{~L}$ of $12 \%$ solution 
D)  $1.5 \mathrm{~L}$ of $18 \%$ solution; $4.5 \mathrm{~L}$ of $12 \%$ solution 
A)  $4 \mathrm{~L}$ of $18 \%$ solution; $2 \mathrm{~L}$ of $12 \%$ solution 
B)  $2.5 \mathrm{~L}$ of $18 \%$ solution; $3.5 \mathrm{~L}$ of $12 \%$ solution 
C)  $2 \mathrm{~L}$ of $18 \%$ solution; $4 \mathrm{~L}$ of $12 \%$ solution 
D)  $1.5 \mathrm{~L}$ of $18 \%$ solution; $4.5 \mathrm{~L}$ of $12 \%$ solution

Question 3

Mardi received an inheritance of $\$ 70,000$. She invested part at $10 \%$ and deposited the remainder in tax- free bonds at 9\%. Her total annual income from the investments was $\$ 6900$. Find the amount invested at $10 \%$.

Accepted Answer

A)  $\$ 59,000$ 
B)  $\$ 63,100$ 
C)  $\$ 60,000$ 
D)  $\$ 30,000$ 
A)  $\$ 59,000$ 
B)  $\$ 63,100$ 
C)  $\$ 60,000$ 
D)  $\$ 30,000$

Question 4

Is the ordered triple a solution to the given system of equations?
-$(-2,-1,5)$
$\mathrm{x}-\mathrm{y}+\mathrm{z}=4$
$2 \mathrm{x}-8 \mathrm{y}-3 \mathrm{z}=24$
$3 x+4 y+2 z=7$.

Accepted Answer

A) True 
 B)False

Question 5

Bob fenced in a rectangular garden in his yard. The length of the rectangle is 4 feet longer than the width and the perimeter is 60 feet. What is the width of the rectangle?

Accepted Answer

A)  12 feet 
B)  13 feet 
C)  26 feet 
D)  15 feet 
A)  12 feet 
B)  13 feet 
C)  26 feet 
D)  15 feet

Question 6

The Family Fine Arts Center charges $\$ 22$ per adult and $\$ 14$ per senior citizen for its performances. On a recent weekend evening when 490 people paid admission, the total receipts were $\$ 7732$. How many who paid were senior citizens?

Accepted Answer

A)  381 senior citizens 
B)  199 senior citizens 
C)  291 senior citizens 
D)  109 senior citizens 
A)  381 senior citizens 
B)  199 senior citizens 
C)  291 senior citizens 
D)  109 senior citizens

Question 7

Solve the system of four equations in four unknowns using matrices.
-$$\begin{aligned} x+y+z & =7500 \
X-z & =-500 \
0)04 x+0.03 y+0.02 z & =220
\end{aligned}$$

Accepted Answer

A)  $(2000,3500,2000)$ 
B)  $(1500,5000,1000)$ 
C)  $(1000,4000,1500)$ 
D)  $(1500,4000,2000)$ 
A)  $(2000,3500,2000)$ 
B)  $(1500,5000,1000)$ 
C)  $(1000,4000,1500)$ 
D)  $(1500,4000,2000)$

Question 8

Graph the system of inequalities.
-$\begin{array}{l}
y \leq 4 x-7 \
y \geq-4 x+9 \
x \leq 3
\end{array}$

Accepted Answer

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

Question 9

Solve the system of equations using matrices.
-$x+y+z=0$
$x-y+2 z=-6$
$2 \mathrm{x}+\mathrm{y}+\mathrm{z}=3$

Accepted Answer

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

Question 10

$9 x-9 y-6 z=-11$
$6 x+3 y-3 z=1$
$\mathrm{x}-\mathrm{y}+2 \mathrm{z}=-3$

Accepted Answer

A)  $\left(-\frac{2}{3}, 1,-\frac{2}{3}\right)$ 
B)  $\left(-\frac{2}{3},-\frac{2}{3}, 1\right)$ 
C)  $\left(\frac{1}{9}, 0,2\right)$ 
D)  $\left(\frac{2}{3}, 1,-\frac{2}{3}\right)$ 
A)  $\left(-\frac{2}{3}, 1,-\frac{2}{3}\right)$ 
B)  $\left(-\frac{2}{3},-\frac{2}{3}, 1\right)$ 
C)  $\left(\frac{1}{9}, 0,2\right)$ 
D)  $\left(\frac{2}{3}, 1,-\frac{2}{3}\right)$

Question 11

A $\$ 86,000$ trust is to be invested in bonds paying $8 \%$, CDs paying $7 \%$, and mortgages paying $9 \%$. The bond and CD investment together must equal the mortgage investment. To earn a $\$ 7180$ annual income from the investments, how much should the bank invest in bonds?

Accepted Answer

A)  $\$ 43,000$ 
B)  $\$ 30,000$ 
C)  $\$ 13,000$ 
D)  $\$ 28,000$ 
A)  $\$ 43,000$ 
B)  $\$ 30,000$ 
C)  $\$ 13,000$ 
D)  $\$ 28,000$

Question 12

Graph the system of inequalities.
-$2 x+y \leq 4$
$\mathrm{y} \leq 1$

Accepted Answer

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

Question 13

Evaluate the determinant
-$\left|\begin{array}{cc}-8 & -12 \ 7 & 4\end{array}\right|$

Accepted Answer

A)  -52 
B)  52 
C)  -116 
D)  1 
A)  -52 
B)  52 
C)  -116 
D)  1

Question 14

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

Accepted Answer

A) True 
 B)False

Question 15

Solve the system of equations using matrices.
-$4 \mathrm{x}-\mathrm{y}-2 \mathrm{z}=-1$
$6 \mathrm{x}+7 \mathrm{y}+7 \mathrm{z}=74$
$-2 x-6 y+z=-19$

Accepted Answer

A)  $(3,5,3)$ 
B)  $(3,3,5)$ 
C)  $(3,-3,5)$ 
D)  $(-3,3,6)$ 
A)  $(3,5,3)$ 
B)  $(3,3,5)$ 
C)  $(3,-3,5)$ 
D)  $(-3,3,6)$

Question 16

A retired couple has $\$ 130,000$ to invest to obtain annual income. They want some of it invested in safe Certificates of Deposit yielding 6\%. The rest they want to invest in AA bonds yielding $11 \%$ per year. How much should they invest in each to realize exactly $\$ 11,800$ per year?

Accepted Answer

A)  $\$ 90,000$ at $11 \%$ and $\$ 40,000$ at $6 \%$ 
B)  $\$ 80,000$ at $11 \%$ and $\$ 50,000$ at $6 \%$ 
C)  $\$ 80,000$ at $6 \%$ and $\$ 50,000$ at $11 \%$ 
D)  $\$ 70,000$ at $6 \%$ and $\$ 60,000$ at $11 \%$ 
A)  $\$ 90,000$ at $11 \%$ and $\$ 40,000$ at $6 \%$ 
B)  $\$ 80,000$ at $11 \%$ and $\$ 50,000$ at $6 \%$ 
C)  $\$ 80,000$ at $6 \%$ and $\$ 50,000$ at $11 \%$ 
D)  $\$ 70,000$ at $6 \%$ and $\$ 60,000$ at $11 \%$

Question 17

Solve the system of equations using Cramer's rule.
-$2 x+7 y=-26.3$
$8 x-5 y=-22.7$

Accepted Answer

A)  $(-4.1,-2.8)$ 
B)  $(-4.7,-2.2)$ 
C)  $(-4.4,2.5)$ 
D)  $(-4.4,-2.5)$ 
A)  $(-4.1,-2.8)$ 
B)  $(-4.7,-2.2)$ 
C)  $(-4.4,2.5)$ 
D)  $(-4.4,-2.5)$

Question 18

$4 x+2 y-3 z=8$
$2 x+4 y+z=36$
$6 \mathrm{x}+2 \mathrm{y}-2 \mathrm{z}=18$

Accepted Answer

A)  $\left(\frac{5}{2}, \frac{13}{2}, 5\right)$ 
B)  $\left(\frac{13}{2},-\frac{5}{2},-5\right)$ 
C)  $\left(\frac{5}{5},-\frac{13}{3}, 5\right)$ 
D)  $\left(-5, \frac{13}{2}, 5\right)$ 
A)  $\left(\frac{5}{2}, \frac{13}{2}, 5\right)$ 
B)  $\left(\frac{13}{2},-\frac{5}{2},-5\right)$ 
C)  $\left(\frac{5}{5},-\frac{13}{3}, 5\right)$ 
D)  $\left(-5, \frac{13}{2}, 5\right)$

Question 19

Evaluate the determinant
-$\left|\begin{array}{rr}-3 & 6 \ -6 & -3\end{array}\right|$

Accepted Answer

A)  -27 
B)  0 
C)  -45 
D)  45 
A)  -27 
B)  0 
C)  -45 
D)  45

Question 20

A rectangular print has a perimeter of 66 inches. The length is 9 inches greater than the width. Find the width of the print.

Accepted Answer

A)  $12 \mathrm{in}$. 
B)  21 in 
C)  $33 \mathrm{in}$. 
D)  $30 \mathrm{in}$. 
A)  $12 \mathrm{in}$. 
B)  21 in 
C)  $33 \mathrm{in}$. 
D)  $30 \mathrm{in}$.

Is the ordered pair a solution of the given system of equations? - left parenthesisminus6commaminus6right parenthesiscomma 2x+y=-6 3x+2y=-6

Mardi received an inheritance of $\$ 70,000$ . She invested part at $10 \%$ and deposited the remainder in tax- free bonds at 9\%. Her total annual income from the investments was $\$ 6900$ . Find the amount invested at $10 \%$ .

Is the ordered triple a solution to the given system of equations? - $(-2,-1,5)$ $\mathrm{x}-\mathrm{y}+\mathrm{z}=4$ $2 \mathrm{x}-8 \mathrm{y}-3 \mathrm{z}=24$ $3 x+4 y+2 z=7$ .

Bob fenced in a rectangular garden in his yard. The length of the rectangle is 4 feet longer than the width and the perimeter is 60 feet. What is the width of the rectangle?

The Family Fine Arts Center charges $\$ 22$ per adult and $\$ 14$ per senior citizen for its performances. On a recent weekend evening when 490 people paid admission, the total receipts were $\$ 7732$ . How many who paid were senior citizens?

Solve the system of four equations in four unknowns using matrices. - x+y+z =7500 X-z =-500 0)04x+0.03y+0.02z =220

Graph the system of inequalities. - y\leq4x-7 y\geq-4x+9 x\leq3 $Graph the system of inequalities. - \begin{array}{l} y \leq 4 x-7 \\ y \geq-4 x+9 \\ x \leq 3 \end{array}$

Solve the system of equations using matrices. - $x+y+z=0$ $x-y+2 z=-6$ $2 \mathrm{x}+\mathrm{y}+\mathrm{z}=3$

$9 x-9 y-6 z=-11$ $6 x+3 y-3 z=1$ $\mathrm{x}-\mathrm{y}+2 \mathrm{z}=-3$

A $\$ 86,000$ trust is to be invested in bonds paying $8 \%$ , CDs paying $7 \%$ , and mortgages paying $9 \%$ . The bond and CD investment together must equal the mortgage investment. To earn a $\$ 7180$ annual income from the investments, how much should the bank invest in bonds?

Graph the system of inequalities. - $2 x+y \leq 4$ $\mathrm{y} \leq 1$ $Graph the system of inequalities. - 2 x+y \leq 4 \mathrm{y} \leq 1$

Evaluate the determinant - $\left|\begin{array}{cc}-8 & -12 \\ 7 & 4\end{array}\right|$

Is the ordered pair a solution of the given system of equations? - left parenthesis2comma3right parenthesiscomma 4x-y=5 2x-4y=-8

Solve the system of equations using matrices. - $4 \mathrm{x}-\mathrm{y}-2 \mathrm{z}=-1$ $6 \mathrm{x}+7 \mathrm{y}+7 \mathrm{z}=74$ $-2 x-6 y+z=-19$

A retired couple has $\$ 130,000$ to invest to obtain annual income. They want some of it invested in safe Certificates of Deposit yielding 6\%. The rest they want to invest in AA bonds yielding $11 \%$ per year. How much should they invest in each to realize exactly $\$ 11,800$ per year?

Solve the system of equations using Cramer's rule. - $2 x+7 y=-26.3$ $8 x-5 y=-22.7$

$4 x+2 y-3 z=8$ $2 x+4 y+z=36$ $6 \mathrm{x}+2 \mathrm{y}-2 \mathrm{z}=18$

Evaluate the determinant - $\left|\begin{array}{rr}-3 & 6 \\ -6 & -3\end{array}\right|$

A rectangular print has a perimeter of 66 inches. The length is 9 inches greater than the width. Find the width of the print.

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 pair a solution of the given system of equations? - left parenthesisminus6commaminus6right parenthesiscomma 2x+y=-6 3x+2y=-6

Mardi received an inheritance of $70,000\$ 70,000$70,000 . She invested part at 10%10 \%10% and deposited the remainder in tax- free bonds at 9\%. Her total annual income from the investments was $6900\$ 6900$6900 . Find the amount invested at 10%10 \%10% .

Is the ordered triple a solution to the given system of equations? - (−2,−1,5)(-2,-1,5)(−2,−1,5) x−y+z=4\mathrm{x}-\mathrm{y}+\mathrm{z}=4x−y+z=4 2x−8y−3z=242 \mathrm{x}-8 \mathrm{y}-3 \mathrm{z}=242x−8y−3z=24 3x+4y+2z=73 x+4 y+2 z=73x+4y+2z=7 .

Bob fenced in a rectangular garden in his yard. The length of the rectangle is 4 feet longer than the width and the perimeter is 60 feet. What is the width of the rectangle?

The Family Fine Arts Center charges $22\$ 22$22 per adult and $14\$ 14$14 per senior citizen for its performances. On a recent weekend evening when 490 people paid admission, the total receipts were $7732\$ 7732$7732 . How many who paid were senior citizens?

Solve the system of four equations in four unknowns using matrices. - x+y+z =7500 X-z =-500 0)04x+0.03y+0.02z =220

Graph the system of inequalities. - y\leq4x-7 y\geq-4x+9 x\leq3

Solve the system of equations using matrices. - x+y+z=0x+y+z=0x+y+z=0 x−y+2z=−6x-y+2 z=-6x−y+2z=−6 2x+y+z=32 \mathrm{x}+\mathrm{y}+\mathrm{z}=32x+y+z=3

9x−9y−6z=−119 x-9 y-6 z=-119x−9y−6z=−11 6x+3y−3z=16 x+3 y-3 z=16x+3y−3z=1 x−y+2z=−3\mathrm{x}-\mathrm{y}+2 \mathrm{z}=-3x−y+2z=−3

Graph the system of inequalities. - 2x+y≤42 x+y \leq 42x+y≤4 y≤1\mathrm{y} \leq 1y≤1

Evaluate the determinant - ∣−8−1274∣\left|\begin{array}{cc}-8 & -12 \\ 7 & 4\end{array}\right|​−87​−124​​

Is the ordered pair a solution of the given system of equations? - left parenthesis2comma3right parenthesiscomma 4x-y=5 2x-4y=-8

Solve the system of equations using matrices. - 4x−y−2z=−14 \mathrm{x}-\mathrm{y}-2 \mathrm{z}=-14x−y−2z=−1 6x+7y+7z=746 \mathrm{x}+7 \mathrm{y}+7 \mathrm{z}=746x+7y+7z=74 −2x−6y+z=−19-2 x-6 y+z=-19−2x−6y+z=−19

Solve the system of equations using Cramer's rule. - 2x+7y=−26.32 x+7 y=-26.32x+7y=−26.3 8x−5y=−22.78 x-5 y=-22.78x−5y=−22.7

4x+2y−3z=84 x+2 y-3 z=84x+2y−3z=8 2x+4y+z=362 x+4 y+z=362x+4y+z=36 6x+2y−2z=186 \mathrm{x}+2 \mathrm{y}-2 \mathrm{z}=186x+2y−2z=18

Evaluate the determinant - ∣−36−6−3∣\left|\begin{array}{rr}-3 & 6 \\ -6 & -3\end{array}\right|​−3−6​6−3​​

A rectangular print has a perimeter of 66 inches. The length is 9 inches greater than the width. Find the width of the print.

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

Mardi received an inheritance of $\$ 70,000$ . She invested part at $10 \%$ and deposited the remainder in tax- free bonds at 9\%. Her total annual income from the investments was $\$ 6900$ . Find the amount invested at $10 \%$ .

Is the ordered triple a solution to the given system of equations? - $(-2,-1,5)$ $\mathrm{x}-\mathrm{y}+\mathrm{z}=4$ $2 \mathrm{x}-8 \mathrm{y}-3 \mathrm{z}=24$ $3 x+4 y+2 z=7$ .

The Family Fine Arts Center charges $\$ 22$ per adult and $\$ 14$ per senior citizen for its performances. On a recent weekend evening when 490 people paid admission, the total receipts were $\$ 7732$ . How many who paid were senior citizens?

Graph the system of inequalities. - y\leq4x-7 y\geq-4x+9 x\leq3 $Graph the system of inequalities. - \begin{array}{l} y \leq 4 x-7 \\ y \geq-4 x+9 \\ x \leq 3 \end{array}$

Solve the system of equations using matrices. - $x+y+z=0$ $x-y+2 z=-6$ $2 \mathrm{x}+\mathrm{y}+\mathrm{z}=3$

$9 x-9 y-6 z=-11$ $6 x+3 y-3 z=1$ $\mathrm{x}-\mathrm{y}+2 \mathrm{z}=-3$

Graph the system of inequalities. - $2 x+y \leq 4$ $\mathrm{y} \leq 1$ $Graph the system of inequalities. - 2 x+y \leq 4 \mathrm{y} \leq 1$

Evaluate the determinant - $\left|\begin{array}{cc}-8 & -12 \\ 7 & 4\end{array}\right|$

Solve the system of equations using matrices. - $4 \mathrm{x}-\mathrm{y}-2 \mathrm{z}=-1$ $6 \mathrm{x}+7 \mathrm{y}+7 \mathrm{z}=74$ $-2 x-6 y+z=-19$

Solve the system of equations using Cramer's rule. - $2 x+7 y=-26.3$ $8 x-5 y=-22.7$

$4 x+2 y-3 z=8$ $2 x+4 y+z=36$ $6 \mathrm{x}+2 \mathrm{y}-2 \mathrm{z}=18$

Evaluate the determinant - $\left|\begin{array}{rr}-3 & 6 \\ -6 & -3\end{array}\right|$