Free Printable Systems of equations

1.

On opening night of the play "Clue" the total attendance was 520 and $1700 was raised. If the cost of an adult ticket, $a$ , was $5 and the cost of a student ticket, $s$ , was $2, which system of equations represent this scenario?

a)

$a+s=1700$
$5a+2s=520$

b)

$a+s=520$
$5a+2s=1700$

c)

$a+s=520$
$5s+2a=1700$

d)

$a+s=1700$
$5s+2a=520$

2.

When shopping for school supplies for her children, Mrs. Michaels bought 2 sets of $\left(m\right)$ markers and 3 $\left(b\right)$ binders for a total cost of $23. Mrs. Laurence bought 5 of the same sets of markers and 3 of the same binders for a total cost $35. Which system of equations represent this scenario?

a)

$2m+3b=35$
$5m+3b=23$

b)

$2b+3m=23$
$5b+3m=35$

c)

$2m+3b=23$
$5m+3b=35$

d)

$2b+3m=35$
$5b+3m=23$

3.

Mark spent $252 on 15 shirts. If t-shirts, $t$ cost him $13 each and dress shirts, $d$ cost him $32 each, which system of equations represent this scenario?

a)

$t+d=252$
$13t+32d=15$

b)

$t+d=15$

13d+32t=252

c)

$t+d=252$

13d+32t=15

d)

$t+d=15$
$13t+32d=252$

4.

At the Maverick Homecoming Football game there was a total attendance of 1490. The cost of an adult ticket, a , was $7 and the cost of a student ticket, s , was $3. If $9030 was raised, which system of equations represent this scenario?

a)

$a+s=1490$
$7s+3a=9030$

b)

$a+s=9030$
$7a+3s=1490$

c)

$a+s=1490$
$7a+3s=9030$

d)

$a+s=9030$
$7s+3a=1490$

5.

Dennis mowed his next door neighbor’s lawn for a handful of dimes and nickels, 80 coins in all. Upon completing the job he counted out the coins and it came to $6.60. Which system of equations could be used to find the exact number of dimes and nickels?

a)

d + n = 6.60
.10d + .05n = 80

b)

d + n = 80
d + n = 6.60

c)

d + n = 80
.10d + .05n = 6.60

d)

d + n = 80
.05d + .10n = 6.60

6.

Solve the system of equations:
x + y + z = 4
x = -2y
z = -3y

a)

(2, -1, 3)

b)

(2, 3, 1)

c)

None of these

d)

(4, 1, -1)

7.

The school that Laura goes to is selling tickets to the annual talent show. On the first day of ticket sales the school sold 4 senior citizen tickets, 2 adult tickets and 5 child tickets for a total of $55. The school took in $67 on the second day by selling 7 senior citizen tickets, 2 adult tickets and 5 child tickets. On the third day the show earned $46 when they sold 2 senior citizen tickets, 4 adult tickets and 2 child tickets. What is the price each of one senior citizen ticket, one adult ticket and one child ticket?

a)

Adult: $12
Child: $8
Senior: $8

b)

Adult: $6
Child: $4
Senior: $5

c)

Adult: $7
Child: $5
Senior: $4

d)

I did not get any of the answers above so I am assuming none ofthe above.

8.

Solve the system of equations:
x + y + z = 4
x = -2y
z = -3y

a)

(2, -1, 3)

b)

(2, 3, 1)

c)

None of these

d)

(4, 1, -1)

9.

Solve the system of equations:

a)

( -2, 3, -3)

b)

None of these

c)

( -2, -3, 3)

d)

( -3, 3, -2)

10.

Solve the system of equations:

a)

( 4, 0, -2)

b)

( -4, -2, 0)

c)

None of these

d)

( -4, 0, -2)

11.

Solve the system of equations:

a)

( 4, 2, -1)

b)

( 4, 3, -1)

c)

None of these

d)

( -4, 3, 1)

12.

Solve the system of equations:

a)

( 5, 1, -4)

b)

(-5, 3, -1)

c)

None of these

d)

( -1, 5, -4)

13.

Solve the system of equations:

a)

( -1, 6, 1)

b)

( 1, 6, -1)

c)

None of these

d)

( -6, -1, 1)

14.

Solve the system of equations:

a)

( -2, 2, 0)

b)

( -2, -2, 0)

c)

( 0, 2, 2)

d)

None of these

15.

Solve the system of equations:

a)

( -2, -3, 4)

b)

( -2, 4, -3)

c)

( 2, -4,3)

d)

None of these

16.

Solve the system of equations:

a)

( -2, 1, -3)

b)

( 2, 3, -1)

c)

No solution

d)

None of these

17.

Solve the system of equations:

a)

( -2, 4, 3)

b)

( 2, 1, 6)

c)

No solution

d)

None of these

18.

The school that Laura goes to is selling tickets to the annual talent show. On the first day of ticket sales the school sold 4 senior citizen tickets, 2 adult tickets and 5 child tickets for a total of $55. The school took in $67 on the second day by selling 7 senior citizen tickets, 2 adult tickets and 5 child tickets. On the third day the show earned $46 when they sold 2 senior citizen tickets, 4 adult tickets and 2 child tickets. What is the price each of one senior citizen ticket, one adult ticket and one child ticket?

a)

Adult: $12
Child: $8
Senior: $8

b)

Adult: $6
Child: $4
Senior: $5

c)

Adult: $7
Child: $5
Senior: $4

d)

I did not get any of the answers above so I am assuming none ofthe above.

19.

Solve the system.

a)

(3, -2, 4)

b)

(2, -3, 1)

c)

(-3, 2, -1)

d)

Infinitely many solutions

20.

Solve the system.

a)

(1, 2, -2)

b)

(1, -3, -2)

c)

(-1, 3, 2)

d)

No Solution

21.

Solve the system of equations:
$6x-4y+5z=31$
$5x+2y+2z=13$
$x+y+z=2$

a)

( -2, 4, 3)

b)

( 2, 1, 6)

c)

$\left(3,-2,1\right)$

d)

None of these

22.

Solve:
-4x - 5y - z = 18
-2x - 5y - 2z = 12
-2x + 5y + 2z = 4

a)

(4, 0, -2)

b)

(-4, 0, -2)

c)

Many Solutions

d)

I did not get any of the answers above so I am assuming none of the above.

23.

Solve the system of equations:

a)

( -2, 4, 3)

b)

( 2, 1, 6)

c)

No solution

d)

infinite # of solutions

24.

Solve the system of equations:

a)

( -2, 3, -3)

b)

None of these

c)

( -2, -3, 3)

d)

( -3, 3, -2)

25.

Solve the system.

a)

(5, -6, 3)

b)

(5, 3, -1)

c)

(5, -6, 5)

d)

No Solution

26.

Solve the system.

a)

(3, -2, 4)

b)

(2, -3, 1)

c)

(-3, 2, -1)

d)

Infinitely many solutions

27.

Solve the system of equations:

a)

( -1, 6, 1)

b)

( 1, 6, -1)

c)

None of these

d)

( -6, -1, 1)

28.

Solve the system of equations:

a)

( 5, 1, -4)

b)

(-5, 3, -1)

c)

None of these

d)

( -1, 5, -4)

29.

Solve the system of equations:

a)

( 4, 0, -2)

b)

( -4, -2, 0)

c)

None of these

d)

( -4, 0, -2)

30.

Solve the system of equations:

a)

( 4, 2, -1)

b)

( 4, 3, -1)

c)

None of these

d)

( -4, 3, 1)

31.

Solve the system of equations:

a)

( -2, 4, 3)

b)

( 2, 1, 6)

c)

No solution

d)

None of these

32.

Solve the system.

a)

(5, -6, 3)

b)

(2, 3, -1)

c)

(-4, 2, 5)

d)

No Solution

33.

Solve the system.
$2x+y=9$
$x-2z=-3$
$2y+3z=15$

a)

(3, -2, 4)

b)

(2, -3, 1)

c)

(3,3,3)

d)

Infinitely many solutions

34.

Solve the System:
$x+y+z=6$
$2x-y+3z=9$
$-x+2y+2z=9$

a)

$\left(3,2,1\right)$

b)

$\left(1,2,3\right)$

c)

$\left(2,1,3\right)$

d)

$\left(2,3,1\right)$

35.

Monica has $1, $5, and $10 bills in her wallet that are worth $96. If she had one more $1 bill, she would have just as many $1 bills as $5 and $10 bills combined. She has 23 bills total. How many of each denomination does she have ?

a)

$\left(7,5,11\right)$

b)

$\left(13,\ 2,8\right)$

c)

$\left(10,8,5\right)$

d)

$\left(11,7,5\right)$

36.

Solve each System:
$2x-y+2z=10$
$4x+2y\ -5z=10$
$x-3y+5z=8$

a)

$\left(4,1,2\right)$

b)

$\left(2,4,2\right)$

c)

$\left(2,2,4\right)$

d)

$\left(4,2,2\right)$

37.

The sum of three numbers is -2. The sum of three times the first number, twice the second number, and the third number is 9. The difference between the second number and half the third number is 10. Find the numbers.

a)

$\left(3,5,-10\right)$

b)

$\left(5,3,-10\right)$

c)

$\left(-10,5,3\right)$

d)

$\left(-10,3,5\right)$

38.

Solve the System:
$2x-3y+z=4$
$-2x+3y-z=-4$
$6x-9y+3z=12$

a)

Infinitely many solutions

b)

$\left(0,2,0\right)$

c)

$\left(2,0,1\right)$

d)

$\left(0,0,2\right)$

39.

Solve:

x + y + z = -1

2x -y +2z= -5

-x +2y -z = 4

a)

(-2,1,-2)

b)

(-5, 3, 1)

c)

Infinitely many solutions

d)

(4, 1, -1)

40.

For :
$x+y\ +z=-1$
$4x+3y+2z=-10$
$2x-4y-2z=-6$
Solve the System

a)

$\left(-3,2,1\right)$

b)

$\left(-2,-3,3\right)$

c)

$\left(-3,-2,4\right)$

d)

$\left(4,-2,-3\right)$

41.

For:
$2x+3y-2z=-1$
$x+5y=9$
$4z-5x=4$
What is the x value?

a)

1

b)

4

c)

0

d)

10

42.

Solve:

x + y +z = 200

z = 2y

12x + 24y + 36z = 6000

a)

(20,60,120)

b)

(60,20,125)

c)

(20,120,60)

d)

(150,60,10)

43.

In a pasture are horses and chickens if there are a total of 28 animals and 80 legs how many chickens and horses?

a)

10 horses, 18 chickens

b)

16 horses, 12 chickens

c)

12 horses, 16 chickens

d)

18 horses, 10 chickens

44.

what is the variable that willl be "eliminated"?

5x - 4y = 11

5x + 4y = -14

a)

x variable

b)

y variables

c)

both variables

45.

what is the resulting combined equation to the following system:

5x - 4y = 11

5x + 4y = -14

a)

5x = -3

b)

10y = -3

c)

10x = -3

d)

10x = -25

46.

what is the resulting combined equation for the system below?

9x + y = 12

-9x + y = 6

a)

-18x = 18

b)

y = 18

c)

2y= 18

d)

18x + 2y = 18

47.

what does the top equation need to be multiplied by to create a zero pair?

2x - 6y = 20

2x + 5y = -11

a)

-1

b)

1

c)

-2

d)

2

48.

2x - 6y = 20

2x + 5y = -11

what would the top equation become when you multiply everything by -1?

a)

2x - 6y = 20

b)

-2x - 6y = -20

c)

-2x + 6y = 20

d)

-2x + 6y = -20

49.

what do you need to multiply the top equation by to make a zero pair:

5x - 2y = 11

-10x + 3y = -4

a)

5

b)

-1

c)

2

d)

-2

50.

Which is the correct substitution for this system?

a)

2(3x -3) = 19

b)

2x + 5y (3x ) = 19

c)

2x + 5(3x-3) = 19

d)

2(3x ) - 3 + 5y = 19

51.

The first step in solving using the substitution method is __________.

a)

get x by itself

b)

get y by itself

c)

get either variable by itself in one equation

d)

add the equations together

52.

y = -6
-3x - 6y = 24

a)

(6, 6)

b)

(6, -6)

c)

(4, -6)

d)

(-6, 4)

53.

What is the solution to the system of equations?

y = 3x - 8

y = 4 - x

a)

(3, 1)

b)

(1, 3)

c)

(-3, 1)

d)

(3, -1)

54.

Solve:
x = -3y - 17
2x + 3y = -7

a)

(1, -20)

b)

(3, 0)

c)

(-5, -2)

d)

(10 , -9)

55.

Solve the system of equations using substitution:
-4x + 4y = 8
y = -2x - 10

a)

(-4, -2)

b)

(12, -34)

c)

(4, -18)

d)

(-2, -6)

56.

Solve using Elimination method.

-3x - 9y = 15

x +3y = - 5

a)

Infinitely Many Solutions

b)

No Solution

c)

(0,0)

d)

(15,0)

e)

(3,9)

57.

Solve the system:
x + 6y = 17
x - 3y = 8

a)

(5, 2)

b)

(11, 1)

c)

(1, 11)

d)

no solution

58.

4x - 5y = 21

x - 3y = 7

a)

(4, -1)

b)

(-4, -1)

c)

(-3, 2)

d)

(1, -3)

59.

6x - 3y = 3
x - 2y = 5

a)

(3, 1)

b)

(1, -3)

c)

(1, 3)

d)

(-1, -3)

60.

What is the solution?

3x + 5y = 13

2x + y = 4

a)

Infinite solutions

b)

(2,1)

c)

(1,2)

d)

No solution

Systems of equations

Total questions: 60

Worksheet time: 9hrs 47mins

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