Deck 7: Systems of Equations

Question 1

Decide whether or not the ordered pair is a solution of the system.

- $(-5,2)$
$\mathrm{x}+\mathrm{y}=-3$
$\mathrm{x}-\mathrm{y}=-7$

Answer 1

True

Question 2

Decide whether or not the ordered pair is a solution of the system.

- $(-2,4)$
$\mathrm{x}+\mathrm{y}=6$
$\mathrm{x}-\mathrm{y}=-2$

Answer 2

False

Question 3

Decide whether or not the ordered pair is a solution of the system.

- $(-5,3)$
$4 \mathrm{x}+\mathrm{y}=-17$
$3 \mathrm{x}+4 \mathrm{y}=-3$

Answer 3

True

Question 4

Decide whether or not the ordered pair is a solution of the system.

- $(1,3)$
$3 \mathrm{x}+\mathrm{y}=0$
$4 \mathrm{x}+3 \mathrm{y}=-5$

Question 5

Decide whether or not the ordered pair is a solution of the system.

- $(-2,2)$
$4 \mathrm{x}=-6-\mathrm{y}$
$3 \mathrm{x}=2-4 \mathrm{y}$

Question 6

Decide whether or not the ordered pair is a solution of the system.

- $(-1,3)$
$2 \mathrm{x}=5-\mathrm{y}$
$3 \mathrm{x}=9-2 \mathrm{y}$

Question 7

Decide whether or not the ordered pair is a solution of the system.

- $(14,4)$
$\mathrm{y}=\frac{2}{7} \mathrm{x}$
$2 \mathrm{x}+\mathrm{y}=32$

Question 8

Decide whether or not the ordered pair is a solution of the system.

- $(12,4)$
$\mathrm{y}=\frac{1}{3} \mathrm{x}$
$2 \mathrm{x}+\mathrm{y}=20$

Question 9

Solve the system by graphing.

-x + y = 7
X - y = -3

A) $(5,2)$
B) Infinite number of solutions
C) No solution
D) $(2,5)$

Question 10

Solve the system by graphing.

- $4 x+y=-14$
$\mathrm{x}+4 \mathrm{y}=4$

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

Question 11

Solve the system by graphing.

- $3 x+y=-10$
$5 x+3 y=-10$

A) $(5,5)$
B) $(-2,-4)$
C) $(-5,-6)$
D) $(-5,5)$

Question 12

Solve the system by graphing.

- $4 x+3 y=11$
$2 x+3 y=7$

A) $(1,2)$
B) $(4,-1)$
C) No solution
D) $(2,1)$

Question 13

Solve the system by graphing.

- $3 x+2 y=5$
$-6 x-4 y=5$

A) No solution
B) $(-1.5,-1)$
C) $(1,1)$
D) $(1.5,-1)$

Question 14

Solve the system by graphing.

- $5 x+y=27$
$5 x+y=42$

A) No solution
B) $(20,7)$
C) Infinite number of solutions
D) $(23,-88)$

Question 15

Solve the system by graphing.

- $3 x+y=16$
$12 x+4 y=64$

A) Infinite number of solutions
B) $(0,16)$
C) No solution
D) $(5,1)$

Question 16

Solve the system by graphing.

- $x=-y$
$y+x=6$

A) $(1,1)$
B) Infinite number of solutions
C) No solution
D) $(1,5)$

Question 17

Solve the system by graphing.

-x = 2
Y = 1

A) $(1,2)$
B) No solution
C) $(2,1)$
D) Infinitely many solutions

Question 18

Solve using the substitution method.

- $x+y=12$
$\mathrm{y}=2 \mathrm{x}+3$

A) $(3,9)$
B) $(4,7)$
C) $(2,12)$
D) $(9,3)$

Question 19

Solve using the substitution method.

- $y=2 x+4$
$3 x+y=34$

A) $(16,6)$
B) $(16,-14)$
C) $(6,16)$
D) $(5,14)$

Question 20

Solve by the substitution method.

- $\begin{aligned} x-4 y & =-27 \\ 4 x-5 y & =-53\end{aligned}$

A) No solution
B) $(-8,6)$
C) $(7,6)$
D) $(-7,5)$

Question 21

Solve by the substitution method.

- $x+2 y=-8$
$2 x+3 y=-12$

A) $(0,-4)$
B) $(4,0)$
C) No solution
D) $(1,-5)$

Question 22

Solve by the substitution method.

- $x+5 y=7$
$-6 x+6 y=-42$

A) $(8,7)$
B) No solution
C) $(-7,-1)$
D) $(7,0)$

Question 23

Solve by the substitution method.

- $8 x-7 y=100$
$3 x-4 y=43$

A) $(8,-3)$
B) $(9,-3)$
C) No solution
D) $(9,-4)$

Question 24

Solve by the substitution method.

- $-5 x+7 y=-35$
$2 \mathrm{x}+2 \mathrm{y}=-10$

A) $(-1,-4)$
B) $(0,-4)$
C) No solution
D) $(0,-5)$

Question 25

Solve by the substitution method.

- $-7 x+9 y=21$
$2 \mathrm{x}+6 \mathrm{y}=-6$

A) $(-4,1)$
B) No solution
C) $(-3,1)$
D) $(-3,0)$

Question 26

Solve by the substitution method.

- $-4 \mathrm{x}-45=7 \mathrm{y}$
$2 \mathrm{x}+4 \mathrm{y}=-26$

A) $(1,-7)$
B) No solution
C) $(1,-6)$
D) $(0,-6)$

Question 27

Solve by the substitution method.

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

A) $(0,0)$
B) $(0,-3)$
C) $(4,-7)$
D) No solution

Question 28

Solve by the substitution method.

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

A) Infinite number of solutions
B) $(0,0)$
C) $(5,4)$
D) $(6,-1)$

Question 29

Solve the problem.

-The sum of two numbers is 45 and their difference is 9 . Find the numbers.

A) 27 and 18
B) 37 and 8
C) 25 and 20
D) 20 and 29

Question 30

Solve the problem.

-The difference between two numbers is 2 . Three times the smaller number minus five times the larger is -34 . What are the numbers?

A) 13 and 15
B) 14 and 16
C) 11 and 13
D) 12 and 14

Question 31

Solve the problem.

-Two angles have a sum of $88^{\circ}$ . Their difference is $22^{\circ}$ . Find the angles.

A) $55^{\circ}$ and $33^{\circ}$
B) $35^{\circ}$ and $57^{\circ}$
C) $53^{\circ}$ and $35^{\circ}$
D) $67^{\circ}$ and $21^{\circ}$

Question 32

Solve the problem.

-The sum of two angles is $191^{\circ}$ . One angle is $28^{\circ}$ less than twice the other. Find the angles.

A) $71^{\circ}$ and $120^{\circ}$
B) $73^{\circ}$ and $118^{\circ}$
C) $114^{\circ}$ and $77^{\circ}$
D) $71^{\circ}$ and $114^{\circ}$

Question 33

Solve the problem.

-The perimeter of a rectangle is $58 \mathrm{~cm}$ . One side is $11 \mathrm{~cm}$ longer than the other side. Find the lengths of the sides.

A) $18 \mathrm{~cm}, 29 \mathrm{~cm}$
B) $9 \mathrm{~cm}, 20 \mathrm{~cm}$
C) $9 \mathrm{~cm}, 11 \mathrm{~cm}$
D) $10 \mathrm{~cm}, 21 \mathrm{~cm}$

Question 34

Solve the problem.

-The perimeter of a rectangle is $54 \mathrm{~m}$ . If the width were doubled and the length were increased by $17 \mathrm{~m}$ , the perimeter would be $104 \mathrm{~m}$ . What are the length and width of the rectangle?

A) width $8 \mathrm{~m}$ , length $13 \mathrm{~m}$
B) width $8 \mathrm{~m}$ , length $19 \mathrm{~m}$
C) width $19 \mathrm{~m}$ , length $8 \mathrm{~m}$
D) width $13 \mathrm{~m}$ , length $13 \mathrm{~m}$

Question 35

Solve the problem.

-The perimeter of a triangle is $45 \mathrm{~cm}$ . The triangle is isosceles now, but if its base were lengthened by $3 \mathrm{~cm}$ and each leg were shortened by $3 \mathrm{~cm}$ , it would be equilateral. Find the base of the original triangle.

A) $14 \mathrm{~cm}$
B) $11 \mathrm{~cm}$
C) $10 \mathrm{~cm}$
D) $17 \mathrm{~cm}$

Question 36

Solve the problem.

-x+y=-11
X-y=3

A) No solution
B) $(4,-6)$
C) $(-5,-6)$
D) $(-4,-7)$

Question 37

Solve using the elimination method.

- $-x-5 y=-35$
$-6 x+5 y=70$

A) $(-8,-5)$
B) $(-5,8)$
C) $(-4,7)$
D) No solution

Question 38

Solve using the elimination method.

- $-x-8 y=-12$
$2 \mathrm{x}+8 \mathrm{y}=8$

A) $(-3,-4)$
B) $(4,1)$
C) No solution
D) $(-4,2)$

Question 39

Solve using the elimination method.

- $3 x-y=17$
$4 \mathrm{x}+\mathrm{y}=25$

A) $(6,1)$
B) $(6,2)$
C) $(1,6)$
D) No solution

Question 40

Solve using the elimination method.

- $-7 x-4 y=-58$
$5 \mathrm{x}+4 \mathrm{y}=46$

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

Question 41

Solve using the elimination method.

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

A) $(3,4)$
B) Infinite number of solutions
C) $(4,4)$
D) No solution

Question 42

Solve by elimination.

- $x+y=14$
$x-y=-2$

A) $(6,8)$
B) $(-6,9)$
C) $(5,9)$
D) No solution

Question 43

Solve by elimination.

- $x-5 y=-31$
$7 x-5 y=-37$

A) $(-1,6)$
B) $(-6,-1)$
C) No solution
D) $(0,5)$

Question 44

Solve by elimination.

- $x-6 y=-59$
$6 \mathrm{x}-7 \mathrm{y}=-93$

A) $(-5,9)$
B) No solution
C) $(-6,10)$
D) $(5,10)$

Question 45

Solve by elimination.

- $x+5 y=-25$
$6 x+6 y=-30$

A) $(0,-5)$
B) $(1,-6)$
C) No solution
D) $(5,0)$

Question 46

Solve by elimination.

- $7 x+5 y=20$
$4 x+3 y=12$

A) $(0,5)$
B) No solution
C) $(0,4)$
D) $(-1,5)$

Question 47

Solve by elimination.

- $8 x-4 y=-16$
$4 \mathrm{x}+2 \mathrm{y}=-8$

A) $(-3,1)$
B) $(-2,0)$
C) $(-2,1)$
D) No solution

Question 48

Solve by elimination.

- $-2 x+6 y=-3$
$-8 x+24 y=-12$

A) $(-18,6)$
B) Infinite number of solutions
C) No solution
D) $(6,-18)$

Question 49

Solve by elimination.

- $4 x-4 y=5$
$-8 x+8 y=10$

A) Infinite number of solutions
B) No solution
C) $(20,-20)$
D) $(-20,20)$

Question 50

Solve by elimination.

- $1.3 x+4 y=-135.3$
$0)03 x-0.13 y=5.77$

A) $(-19,40)$
B) $(20,-41)$
C) $(-20,-36)$
D) $(19,-40)$

Question 51

Solve by elimination.

- $x+\frac{1}{4} y=-\frac{23}{30}$

$\frac{1}{4} x-y=\frac{371}{60}$

A) $\left(\frac{11}{15},-6\right)$

B) $\left(6, \frac{11}{15}\right)$

C) $\left(-6,-\frac{11}{15}\right)$

D) $\left(\frac{11}{15}, 6\right)$

Question 52

Solve the problem.

-Two angles are supplementary, and one is $40^{\circ}$ more than three times the other. Find the smaller angle.

A) $75^{\circ}$
B) $35^{\circ}$
C) $145^{\circ}$
D) $105^{\circ}$

Question 53

Solve the problem.

-In a right triangle, one acute angle is $54^{\circ}$ more than twice the other. Find each acute angle.

A) $21^{\circ}$ and $69^{\circ}$
B) $37^{\circ}$ and $53^{\circ}$
C) $28^{\circ}$ and $62^{\circ}$
D) $12^{\circ}$ and $78^{\circ}$

Question 54

Solve the problem.

-Two angles are supplementary, and one is $5^{\circ}$ more than six times the other. Find the larger angle.

A) $70^{\circ}$
B) $155^{\circ}$
C) $25^{\circ}$
D) $110^{\circ}$

Question 55

Solve the problem.

-Best Rentals charges a daily fee plus a mileage fee for renting its cars. Barney was charged $\$ 99$ for 3 days and 300 miles, while Mary was charged $\$ 178$ for 5 days and 600 miles. What does Best Rental charge per day and per mile?

A) $\$ 20$ per day and $13 \notin$ per mile
B) $\$ 13$ per day and $20 \notin$ per mile
C) $\$ 19$ per day and $14 \notin$ per mile
D) $\$ 21$ per day and $14 \notin$ per mile

Question 56

Solve the problem.

-There were 33,000 people at a ball game in Los Angeles. The day's receipts were $\$ 245,000$ . How many people paid $\$ 13$ for reserved seats and how many paid $\$ 5$ for general admission?

A) 10,000 paid $\$ 13$ and 23,000 paid $\$ 5$
B) 13,000 paid $\$ 13$ and 20,000 paid $\$ 5$
C) 20,000 paid $\$ 13$ and 13,000 paid $\$ 5$
D) 23,000 paid $\$ 13$ and 10,000 paid $\$ 5$

Question 57

Solve the problem.

-There were 480 people at a play. The admission price was $\$ 2$ for adults and $\$ 1$ for children. The admission receipts were $\$ 740$ . How many adults and how many children attended?

A) 185 adults and 295 children
B) 220 adults and 260 children
C) 260 adults and 220 children
D) 110 adults and 370 children

Question 58

Solve the problem.

-A salesman sold $\$ 400$ more than the rest of the sales staff. If the sales total for the day was $\$ 1600$ , how much did the rest of the sales staff sell?

A) $\$ 1000$
B) $\$ 1200$
C) $\$ 600$
D) $\$ 800$

Question 59

Solve the problem.

-Joe has a collection of nickels and dimes that is worth $\$ 4.45$ . If the number of dimes were doubled and the number of nickels were increased by 15 , the value of the coins would be $\$ 7.30$ . How many dimes does he have?

A) 15 dimes
B) 21 dimes
C) 10 dimes
D) 47 dimes

Question 60

Solve the problem.

-Mrs. Boyd has a desk full of quarters and nickels. If she has a total of 20 coins with a total face value of $\$ 2.40$ , how many of the coins are nickels?

A) 7 nickels
B) 15 nickels
C) 12 nickels
D) 13 nickels

Question 61

Solve the problem.

-Andy has 34 coins made up of quarters and half dollars, and their total value is $\$ 13.50$ . How many quarters does he have?

A) 20 quarters
B) 19 quarters
C) 22 quarters
D) 14 quarters

Question 62

Solve the problem.

-Ron and Kathy are ticket- sellers at their class play, Ron handling student tickets that sell for $\$ 1.00$ each and Kathy selling adult tickets for $\$ 3.50$ each. If their total income for 38 tickets was $\$ 83.00$ , how many did Ron sell?

A) 18 tickets
B) 23 tickets
C) 22 tickets
D) 20 tickets

Question 63

Solve the problem.

-Helen Weller invested $\$ 10,000$ in an account that pays $12 \%$ simple interest. How much additional money must be invested in an account that pays 15\% simple interest so that the total interest is equal to the interest on the two investments at the rate of $13 \%$ ?

A) $\$ 6000$
B) $\$ 7000$
C) $\$ 10,000$
D) $\$ 5000$

Question 64

Solve the problem.

-Roberto invested some money at $6 \%$ , and then invested $\$ 5000$ more than twice this amount at $11 \%$ . His total annual income from the two investments was $\$ 4750$ . How much was invested at $11 \%$ ?

A) $\$ 35,000$
B) $\$ 30,000$
C) $\$ 3500$
D) $\$ 15,000$

Question 65

Solve the problem.

-Tim and Judy mix two kinds of feed for pedigreed dogs. They wish to make 21 pounds of feed worth $\$ 0.17$ per pound by mixing one kind worth $\$ 0.11$ per pound with another worth $\$ 0.22$ per pound. How many pounds of the cheaper kind should they use in the mix? Round to the nearest whole pound if necessary.

A) 10 pounds
B) 12 pounds
C) 16 pounds
D) 11 pounds

Question 66

Solve the problem.

-Ellen wishes to mix candy worth $\$ 1.11$ per pound with candy worth $\$ 3.86$ per pound to form 16 pounds of a mixture worth $\$ 2.31$ per pound. How many pounds of the more expensive candy should she use?

A) 12 pounds
B) 9 pounds
C) 11 pounds
D) 7 pounds

Question 67

Solve the problem.

-A contractor mixes concrete from bags of pre- mix for small jobs. How many bags with $4 \%$ cement should he mix with 7 bags of $20 \%$ cement to produce a mix containing $11 \%$ cement?

A) 21 bags
B) 11 bags
C) 16 bags
D) 9 bags

Question 68

Solve the problem.

-How many liters of a $30 \%$ alcohol solution must be mixed with 60 liters of a $70 \%$ solution to get a $40 \%$ solution?

A) $18 \mathrm{~L}$
B) $180 \mathrm{~L}$
C) $240 \mathrm{~L}$
D) $24 \mathrm{~L}$

Question 69

Solve the problem.

-In a chemistry class, 5 liters of a $4 \%$ silver iodide solution must be mixed with a $10 \%$ solution to get a $6 \%$ solution. How many liters of the $10 \%$ solution are needed?

A) $1.5 \mathrm{~L}$
B) $5.0 \mathrm{~L}$
C) $2.5 \mathrm{~L}$
D) $3.5 \mathrm{~L}$

Question 70

Solve the problem.

-A merchant has coffee worth $\$ 40$ a pound that she wishes to mix with 80 pounds of coffee worth $\$$ 70 a pound to get a mixture that can be sold for $\$ 50$ a pound. How many pounds of the $\$ 40$ coffee should be used?

A) $80 \mathrm{lb}$
B) $240 \mathrm{lb}$
C) $120 \mathrm{lb}$
D) $160 \mathrm{lb}$

Question 71

Solve the problem.

-A boat traveled for $3 \mathrm{hr}$ with a 3- $\mathrm{mph}$ current to reach a picnic area. The return trip against the same current took $6 \mathrm{hr}$ . Find the speed of the boat in still water.

A) $36 \mathrm{mph}$
B) $21 \mathrm{mph}$
C) $12 \mathrm{mph}$
D) $9 \mathrm{mph}$

Question 72

Solve the problem.

-Kevin walks and jogs to his favorite coffee shop to study each weekend. He averages $3 \mathrm{mph}$ walking and $5 \mathrm{mph}$ jogging. The distance from his home to the coffee shop is $14 \mathrm{mi}$ , and he makes the trip in $4 \mathrm{hr}$ . How long does Kevin jog?

A) $4 \mathrm{hr}$
B) $2 \mathrm{hr}$
C) $3 \mathrm{hr}$
D) $1 \mathrm{hr}$

Question 73

Solve the problem.

-An airplane took $5 \mathrm{hr}$ to fly $600 \mathrm{mi}$ against a head wind. The return trip with the same wind took 1 $\mathrm{hr}$ . Find the speed of the plane in still air.

A) $240 \mathrm{mph}$
B) $360 \mathrm{mph}$
C) $120 \mathrm{mph}$
D) $600 \mathrm{mph}$

Question 74

Solve the problem.

-Rachael's bike got a flat tire and she must walk the rest of the way to work. The bike was being ridden at $9 \mathrm{mph}$ , and Rachael walks at a speed of $4 \mathrm{mph}$ . The distanœ from home to work is $22 \mathrm{mi}$ , and the total time for the trip was $3 \mathrm{hr}$ . How far did she have to walk?

A) $1 \mathrm{mi}$
B) $18 \mathrm{mi}$
C) $2 \mathrm{mi}$
D) $4 \mathrm{mi}$

Question 75

Solve the problem.

-Two cars leave town at the same time going in the same direction. One travels at $40 \mathrm{mph}$ and the other travels at $52 \mathrm{mph}$ . In how many hours will they be $48 \mathrm{mi}$ apart?

A) $1 \mathrm{hr}$
B) $40 \mathrm{hr}$
C) $4 \mathrm{hr}$
D) $12 \mathrm{hr}$

Question 76

Solve the problem.

-A private airplane leaves an airport and flies due east at $185 \mathrm{mph}$ . Two hours later, a jet leaves the same airport and flies due east at $333 \mathrm{mph}$ . When will the jet overtake the plane?

A) $2 \frac{1}{2} \mathrm{hr}$
B) $1 \frac{4}{5} \mathrm{hr}$
C) $\frac{5}{9} \mathrm{hr}$
D) $4 \frac{1}{2} \mathrm{hr}$

Question 77

Solve the problem.

-The speed of a stream is $4 \mathrm{mph}$ . If a boat travels 40 miles downstream in the same time that it takes to travel 20 miles upstream, what is the speed of the boat in still water?

A) $12 \mathrm{mph}$
B) $8 \mathrm{mph}$
C) $15 \mathrm{mph}$
D) $14 \mathrm{mph}$

Question 78

Solve the problem.

-A plane flies 420 miles with the wind and 320 miles against the wind in the same length of time. If the speed of the wind is $30 \mathrm{mph}$ , what is the speed of the plane in still air?

A) $247 \mathrm{mph}$
B) $222 \mathrm{mph}$
C) $212 \mathrm{mph}$
D) $227 \mathrm{mph}$

Question 79

Solve the problem.

-From a point on a river, two boats are driven in opposite directions, one at 9 miles per hour and the other at 6 miles per hour. In how many hours will they be 60 miles apart?

A) $4 \mathrm{hr}$
B) $5 \mathrm{hr}$
C) $6 \mathrm{hr}$
D) $1 \mathrm{hr}$

Question 80

Solve the problem.

-Candy and Delvis are riding bicycles in the same direction. Candy is traveling at the speed of 6 miles per hour, and Delvis is traveling at the speed of 12 miles per hour. In 4 hours what is the distance between them?

A) $24 \mathrm{mi}$
B) $33 \mathrm{mi}$
C) $25 \mathrm{mi}$
D) $21 \mathrm{mi}$