Deck 4: Systems of Equations

Question 1

Is the ordered pair a solution of the given system of equations?

- $(-2,-1) ,\begin{aligned} & x+y=-3 \\ & x-y=-1\end{aligned}$

Answer 1

True

Question 2

Is the ordered pair a solution of the given system of equations?

- $(3,3), \begin{aligned} & x+y=0 \\ & x-y=-6\end{aligned}$

Answer 2

False

Question 3

Is the ordered pair a solution of the given system of equations?

- $(2,-4), \begin{aligned} & 3 x+y=2 \\ & 4 x+3 y=-4\end{aligned}$

Answer 3

True

Question 4

Is the ordered pair a solution of the given system of equations?

- $(-6,-6), \begin{aligned} & 2 x+y=-6 \\ & 3 x+2 y=-6\end{aligned}$

Question 5

Is the ordered pair a solution of the given system of equations?

- $(2,3), \begin{aligned} & 4 x-y=5 \\ & 2 x-4 y=-8\end{aligned}$

Question 6

Is the ordered pair a solution of the given system of equations?

- $(-3,-2), \begin{aligned} & 3 x-y=7 \\ & 2 x-3 y=0\end{aligned}$

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 $x$ .

- $\begin{aligned} y & =x-4 \\ y & =-x+16\end{aligned}$

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

Question 8

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 $x$ .

- $4 x+y=-14$
$x+4 y=-11$

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

Question 9

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 $x$ .

- $\begin{array}{l}y=34-5 x \\x+5 y=26\end{array}$

A) $(7,-1)$
B) $(-6,4)$
C) $(6,5)$
D) $(6,4)$

Question 10

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 $x$ .

- $x=y-6$
$6 x=3 y$

A) $(12,6)$
B) $(-6,0)$
C) $(0,0)$
D) $(6,12)$

Question 11

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 $x$ .

- $x=2$
$y=4$

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

Question 12

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 $x$ .

- $3 x-2 y=-4$
$-2 x+3 y=16$

A) $(8,4)$
B) $(3,22)$
C) Inconsistent, $\varnothing$
D) $(4,8)$

Question 13

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 $x$ .

- $9 x+y=23$
$9 x+y=77$

A) $(18,5)$
B) Dependent, $(\mathrm{x},-9 \mathrm{x}+23)$
C) Inconsistent, $\varnothing$
D) $(21,-166)$

Question 14

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 $x$ .

- $3 x+y=13$
$9 x+3 y=39$

A) Dependent, ( $\mathrm{x},-3 \mathrm{x}+13)$
B) $(5,-2)$
C) Inconsistent, $\varnothing$
D) $(0,13)$

Question 15

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 $x$ .

- $3 \mathrm{x}-2 \mathrm{y}=4$
$-6 x+4 y=7$

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

Question 16

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 $x$ .

- $4 x+2 y=40$
$-2 x+4 y=20$

A) $(8,6)$
B) Inconsistent, $\varnothing$
C) $(6,8)$
D) $(4,28)$

Question 17

When two linear equations are solved for $y$ and the slopes are equal and the $y$ - intercepts are different, the lines are

A) Intersecting
B) One Graph
C) Parallel

Question 18

When two linear equations are solved for $y$ and the slopes are different and the y-intercepts are different, the lines are ?

A) Intersecting
B) One Graph
C) Parallel

Question 19

If the $y$ term is missing in both of two linear equations, the lines are ?

A) Parallel
B) Parallel or One Graph
C) Intersecting
D) One Graph

Question 20

A student was asked to find ordered pairs that solve the system of equations
$$\begin{gathered}X+2 y=3 \\2 x+4 y=6\end{gathered}$$
The student claims that $(1,1)$ and $(-1,2)$ are the only solutions. Is the student correct?

Question 21

Why could $(5,-3)$ not be a solution of the system that is graphed?

Question 22

Draw the graph of a linear equation that, along with the given line, forms an inconsistent system.

Question 23

Draw the graph of a linear equation that, along with the given line, forms a dependent system.

Question 24

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

Question 25

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 $x$ .

- $x=-17-5 y$
$-2 \mathrm{x}+4 \mathrm{y}=-22$

A) $(-3,-3)$
B) $(3,-4)$
C) $(2,-3)$
D) Inconsistent, $\varnothing$

Question 26

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 $x$ .

- $x=4-4 y$
$3 x+5 y=5$

A) $(1,0)$
B) $(0,1)$
C) $(-1,0)$
D) Inconsistent, $\varnothing$

Question 27

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 $x$ .

- $y=13-3 x$
$2 \mathrm{x}+9 \mathrm{y}=-8$

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

Question 28

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 $x$ .

- $5 y+x=-5$
$\mathrm{x}=2 \mathrm{y}-6$

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 29

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 $x$ .

- $y=6 x+40$
$7 x+5 y=-59$

A) $(-7,-2)$
B) $(7,2)$
C) Dependent, $(x, 6 x+40)$
D) Inøonsistent, $\varnothing$

Question 30

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 $x$ .

- $x-5 y=3$
$x=9+5 y$

A) $(3,0)$
B) $(3,5)$
C) Dependent, $(x, 5 x+3)$
D) Inconsistent, $\varnothing$

Question 31

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 $x$ .

- $4 \mathrm{x}-1=\mathrm{y}$
$y-4 x=1$

A) $(0,0)$
B) $(4,1)$
C) Dependent, ( $x, 4 x-1)$
D) Inconsistent, $\varnothing$

Question 32

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 $x$ .

- $x+y=11$
$\mathrm{x}-\mathrm{y}=3$

A) $(6,5)$
B) $\varnothing$
C) $(-7,5)$
D) $(7,4)$

Question 33

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 $x$ .

- $x+8 y=51$
$-4 x+7 y=69$

A) $\varnothing$
B) $(-6,8)$
C) $(5,8)$
D) $(-5,7)$

Question 34

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 $x$ .

- $7 x-5 y=20$
$-4 \mathrm{x}+3 \mathrm{y}=-12$

A) $(0,-4)$
B) $\varnothing$
C) $(-1,-3)$
D) $(0,-3)$

Question 35

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 $x$ .

- $2 x-7 y=6$
$4 x-14 y=30$

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

Question 36

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 $x$ .

- $\begin{aligned} & 2 x+7 y=-25 \\ & 7 x+3 y=-23\end{aligned}$

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

Question 37

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 $x$ .

- $x+y=9$
$\mathrm{x}+\mathrm{y}=-1$

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

Question 38

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 $x$ .

- $x+y=4$
$4 \mathrm{x}+4 \mathrm{y}=16$

A) $(x,-x+4)$
B) $\varnothing$
C) $(4,0)$
D) $(0,0)$

Question 39

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 $x$ .

- $\frac{1}{5} \mathrm{x}-\frac{1}{4} \mathrm{y}=3$
$\frac{2}{5} x+\frac{1}{2} y=2$

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

Question 40

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 $x$ .

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

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

Question 41

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 $x$ .

- $0.9 x+0.2 y=4.2$
$\mathrm{x}-0.1 \mathrm{y}=3.7$

A) $(0.4,0.3)$
B) $\varnothing$
C) $(3,4)$
D) $(4,3)$

Question 42

For the given system of equations, which method would be the most efficient method to use when solving the system of equations: substitution, addition, or either?

- $6 x-5 y=34$
$4 \mathrm{x}+3 \mathrm{y}=28$

A) substitution
B) addition
C) either

Question 43

For the given system of equations, which method would be the most efficient method to use when solving the system of equations: substitution, addition, or either?

- $y=-\frac{1}{2} x-5$
$3 \mathrm{x}+7 \mathrm{y}=19$

A) addition
B) substitution
C) either

Question 44

For the given system of equations, which method would be the most efficient method to use when solving the system of equations: substitution, addition, or either?

- $x+y=12$
$4 \mathrm{x}+9 \mathrm{y}=41$

A) addition
B) substitution
C) either

Question 45

Solve by addition or substitution.

- $x+7 y=7$
$4 \mathrm{x}-5 \mathrm{y}=-5$

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

Question 46

Solve by addition or substitution.

- $x+y=15$
$\mathrm{x}-\mathrm{y}=-3$

A) $(6,9)$
B) $(-6,10)$
C) $(5,10)$
D) $\varnothing$

Question 47

Solve by addition or substitution.

- $3 y+x=9$
$\mathrm{x}=4 \mathrm{y}+2$

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

Question 48

Solve by addition or substitution.

- $x+2 y=-4$
$-5 x+2 y=32$

A) $(-5,0)$
B) $(-1,-6)$
C) $(-6,1)$
D) $\varnothing$

Question 49

Solve by addition or substitution.

- $x+9 y=59$
$2 \mathrm{x}+9 \mathrm{y}=64$

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

Question 50

Solve by addition or substitution.

- $x-2 y=-7$
$2 \mathrm{x}-3 \mathrm{y}=-13$

A) $(5,2)$
B) $(-6,2)$
C) $(-5,1)$
D) $\varnothing$

Question 51

Solve by addition or substitution.

- $-4 x+2 y=3$
$4 \mathrm{x}-2 \mathrm{y}=3$

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 52

Solve by addition or substitution.

- $7 x+9 y=9$
$4 x+7 y=7$

A) $(0,2)$
B) $(0,1)$
C) $(-1,2)$
D) $\varnothing$

Question 53

Solve by addition or substitution.

- $9 x+7 y=-36$
$4 \mathrm{x}-2 \mathrm{y}=-16$

A) $(-5,1)$
B) $(-4,1)$
C) $(-4,0)$
D) $\varnothing$

Question 54

Solve by addition or substitution.

- $\frac{1}{5} x-\frac{1}{4} y=3$
$\frac{2}{5} x+\frac{1}{2} y=2$

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

Question 55

Andy has 15 coins made up of quarters and half dollars, and their total value is $\$ 5.50$ . How many quarters does he have?

A) 13 quarters
B) 8 quarters
C) 7 quarters
D) 9 quarters

Question 56

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

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

Question 57

A woman made a deposit of $\$ 127$ . If her deposit consisted of 43 bills, some of them one dollar bills and the rest being five- dollar bills, how many one- dollar bills did she deposit?

A) 21 one dollar bills
B) 17 one- dollar bills
C) 12 one dollar bills
D) 22 one- dollar bills

Question 58

A paper boy collected \$7.55, part in nickels and part in dimes. If the number of nickels was 6 more than one- half the number of dimes, how many nickels were there?

A) 58 nickels
B) 35 nickels
C) 45 nickels
D) 68 nickels

Question 59

Don runs a charity fruit sale, selling boxes of oranges for $\$ 11$ and boxes of grapefruit for $\$ 10$ . If he sold a total of 762 boxes and took in $\$ 8125$ in all, then how many boxes of oranges did he sell?

A) 458 boxes
B) 257 boxes
C) 505 boxes
D) 383 boxes

Question 60

In a basketball game, Will scored 36 points, consisting only of three-point shots and two-point shots. He made a total of 16 shots. How many shots of each type did he make?

A) Two- point shots: 11; three- point shots: 5
B) Two- point shots: 13; three point shots: 3
C) Two- point shots: 12; three point shots: 4
D) Two- point shots: 4; three- point shots: 12

Question 61

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

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 62

The sum of two angles is $136^{\circ}$ . One angle is $20^{\circ}$ less than twice the other. Find the angles.

A) $50^{\circ}$ and $86^{\circ}$
B) $52^{\circ}$ and $84^{\circ}$
C) $80^{\circ}$ and $56^{\circ}$
D) $50^{\circ}$ and $80^{\circ}$

Question 63

Two angles are supplementary. One angle is $52^{\circ}$ less than three times the other. Find the measures of the angles.

A) $30^{\circ}, 38^{\circ}$
B) $58^{\circ}, 122^{\circ}$
C) $53^{\circ}, 127^{\circ}$
D) $63^{\circ}, 117^{\circ}$

Question 64

Two angles are complementary. The sum of the first angle plus twice the second angle is $153^{\circ}$ . Find the measures of the angles.

A) $1^{\circ}, 76^{\circ}$
B) $22^{\circ}, 68^{\circ}$
C) $27^{\circ}, 63^{\circ}$
D) $117^{\circ}, 63^{\circ}$

Question 65

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

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 66

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?

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 67

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?

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

Question 68

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 $10 \%$ .

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

Question 69

Walt made an extra $\$ 7000$ last year from a part- time job. He invested part of the money at $7 \%$ and the rest at $10 \%$ . He made a total of $\$ 580$ in interest. How much was invested at $10 \%$ ?

A) $\$ 4000$
B) $\$ 3000$
C) $\$ 3500$
D) $\$ 7000$

Question 70

A student took out two loans totaling $\$ 15,000$ to help pay for college expenses. One loan was at $10 \%$ simple interest, and the other was at $5 \%$ . After one year, the student owed $\$ 1250$ in interest. Find the amount of the loan at $5 \%$ .

A) $\$ 5000$
B) $\$ 1000$
C) $\$ 250$
D) $\$ 10,000$

Question 71

Roberto invested some money at 8\%, and then invested $\$ 2000$ more than twice this amount at $10 \%$ . His total annual income from the two investments was $\$ 4120$ . How much was invested at $10 \%$ ?

A) $\$ 3000$
B) $\$ 6000$
C) $\$ 28,000$
D) $\$ 30,000$

Question 72

Helen Weller invested $\$ 14,000$ in an account that pays $12 \%$ APR. How much additional money must be invested in an aocount that pays an APR of $15 \%$ so that the total interest is equal to the interest on the two investments at the rate of $13 \%$ ?

A) $\$ 14,000$
B) $\$ 10,000$
C) $\$ 7000$
D) $\$ 11,000$

Question 73

Paul invested four times as much money in an account paying $7 \%$ interest than he did in an account paying $1 \%$ interest. If the total interest paid was $\$ 870$ , how much did he invest in each?

A) $\$ 120$ at $7 \%$ , $\$ 30$ at $1 \%$
B) $\$ 12,000$ at $7 \%, \$ 3000$ at $1 \%$
C) $\$ 12,000$ at $7 \%, \$ 3500$ at $1 \%$
D) $\$ 3000$ at $7 \%, \$ 12,000$ at $1 \%$

Question 74

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?

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 75

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?

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

Question 76

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?

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

Question 77

How many liters of a $30 \%$ - alcohol solution must be mixed with 40 liters of a solution that is $60 \%$ alcohol to get a solution that is $50 \%$ alcohol?

A) $6 \mathrm{~L}$
B) $2 \mathrm{~L}$
C) $60 \mathrm{~L}$
D) $20 \mathrm{~L}$

Question 78

In a chemistry class, 6 liters of a $4 \%$ - saline solution must be mixed with a $10 \%$ solution to get a $6 \%$ solution. How many liters of the $10 \%$ solution are needed?

A) $6.0 \mathrm{~L}$
B) $4.0 \mathrm{~L}$
C) $2.0 \mathrm{~L}$
D) $3.0 \mathrm{~L}$

Question 79

How many liters (L) of a $10 \%$ silver iodide solution must be mixed with $6 \mathrm{~L}$ of a $4 \%$ silver iodide solution to get a $6 \%$ solution?

A) $6.0 \mathrm{~L}$
B) $3.0 \mathrm{~L}$
C) $4.0 \mathrm{~L}$
D) $2.0 \mathrm{~L}$

Question 80

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.

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 $93 \%$