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System of equations

Total questions: 75

Worksheet time: 6hrs 37mins

Name
Class
Date
1.
What is the solution to the system?
a)
(0, 3)
b)
(1, -1)
c)
(-3, 1)
d)
(1, 3)
2.
What is the solution? 
a)
1
b)
-2
c)
(1, 2)
d)
(1, -1)
3.
What is the solution?
a)
(6, 3)
b)
(3, 6)
c)
(-6, 3)
d)
No solution
4.
Parallel Lines never intersect because...
a)
they have the same slopes. 
b)
they have the same y-intercept.
c)
they have different slopes.
d)
they have different y-intercepts. 
5.
Does the system have one, none or infinite solutions?
8x + 4y = 12
y = -2x + 3
a)
(0,3)
b)
(3,0)
c)
No solution(parallel lines)
d)
Infinitely many solutions
6.

2x - y = 0

4x - y = 0

a)

(1,2)

b)

(0,0)

c)

No Solutions

d)

Infinite Solutions

7.



How many solutions?
a)
One Solution
b)
No solution
c)
Infinitely Many Solutions
8.
Solve for x and y.
y = 2/3x - 2
y = -x + 3
a)
(0,3)
b)
(0,-3)
c)
(3,0)
d)
(-3,0)
9.
Solve for x and y
3x + 2y = 16
7x + y = 19
a)
(-2,5)
b)
(-2,-5)
c)
(2,-5)
d)
(2,5)
10.

2x - y = 0

4x - y = 0

a)

(1,2)

b)

(0,0)

c)

No Solutions

d)

Infinite Solutions

11.
The equations of two lines are:
 2x-y=4 and y=-2x+8.
What is the value of x in the solution for this system?
a)
x=8
b)
x=3
c)
x=11
d)
x=5
12.
If a system of equations has no solution, what does the graph look like? 
a)
intersecting lines
b)
parallel lines
c)
skew lines
d)
intersecting lines
13.
What is the value of the y-coordinate of the solution to the system of equations 
x-2y=1
x+4y=7 
a)
1
b)
-1
c)
3
d)
4
14.
What is the solution?
a)
One Solution
b)
No solution
c)
Infinitely Many Solutions
15.
What is the solution?
a)
(1, -1)
b)
(-1, 1)
c)
(0, -2)
d)
(2, 0)
16.
Solve the following system by setting the two equations equal to each other.  What is the solution?
HINT:  - 1/3x + 4 = 2/3x + 1 and then solve for x.  Once you find x go back and find y.
a)
Infinite number of solutions
b)
(3, 3)
c)
(3, -3)
d)
(-3, 3)
17.
Solve:
3x + 2y = 16
7x + y = 19
a)
(-2,5)
b)
(-2,-5)
c)
(2,-5)
d)
(2,5)
18.

2x - y = 0

4x - y = 0

a)

(1,2)

b)

(0,0)

c)

No Solutions

d)

Infinite Solutions

19.
Which of the following is not a method to solve systems?
a)
Elimination
b)
Difference of Squares
c)
Substitution
d)
Graphing
20.
Solve for x and y
3x + 2y = 16
7x + y = 19
a)
(-2,5)
b)
(-2,-5)
c)
(2,-5)
d)
(2,5)
21.
What is the solution to this system?
y = 2x + 1
y = 4x - 1
a)
(1,3)
b)
(-1,-3)
c)
(-1,3)
d)
(3,1)
22.
What is the solution to this system?
y = 2/3x - 2
y = -x + 3
a)
(0,3)
b)
(0,-3)
c)
(3,0)
d)
(-3,0)
23.
What is the solution to this system?
x - y = 6
y= 2x - 5
a)
(1,3)
b)
(-1,3)
c)
(-1,-7)
d)
(1,-7)
24.
Solve:
y = 7x + 9
2y + 2x = -18
a)
(5, 0)
b)
(9, 18)
c)
(-2, -5)
d)
(1, 16)
25.
Solve by elimination:
4x+9y=28
-4x-y=-28
a)
(-7,0)
b)
(6,0)
c)
(-6,0)
d)
(7,0)
26.
Solve by elimination:
3x+7y=23

-3x-7y=-17
a)
No solution
b)
ARN
c)
(-3,3)
d)
(3,3)
27.
Solve by elimination 
-12x-10y= 0 
 6x+5y= -1
a)
infinite solutions
b)
(0,0)
c)
no solution 
d)
(2,1)
28.



How many solutions?
a)
One Solution
b)
No solution
c)
Infinitely Many Solutions
29.
What is the solution? 
a)
1
b)
-2
c)
(1, 2)
d)
(1, -1)
30.
What is the solution to the system?
a)
(0, 3)
b)
(1, -1)
c)
(-3, 1)
d)
(1, 3)
31.

Which point satisfies both equations?


y - x = 2

y + 2x = 2

a)

(0, 2)

b)

(2, 0)

c)

(2, 4)

d)

(-2, 6)

32.

A jar contains only nickels and quarters. The total number of coins in the jar is 15. The total value of the coins is $2.35. Which system of equations represents this situation?

a)

n + q = 2.35

.05n + .25q = 15

b)

n + q = 15

.5n + .25q = 15

c)

n + q =15

.05n + .25q = 2.35

d)

.05n + q = 15

n + .25q = 2.35

33.

The graphs of two equations are shown. Which statement is true about the solution of this system of equations?

a)

The solution is a line.

b)

The solution is a point.

c)

There are no solutions.

d)

There are infinitely many solutions.

34.

At which point do the graphs of these equations intersect?

4x + 3y = 12

2x - 5y = -20

a)

(0, 4)

b)

(4, 0)

c)

The graphs do not intersect.

d)

The graphs represent the same line

35.

The cost for renting kayaks at Company A is c = 5h + 20. The cost for renting at Company B is c = 7h + 12. What is the number of rental hours for which the cost will be the same for both companies?

a)

4 hours

b)

5 hours

c)

8 hours

d)

16 hours

36.

Line m passes through the points (0, -1) and (-3, 5). Which pair of coordinates is on a line that is parallel to line m?

(HINT: Find the slope between each set of points. What do we know about the slopes of parallel lines?)

a)

(1, 6) and (-4, 1)

b)

(2, 3) and (-1, 9)

c)

(-1, 1) and (-5, 7)

d)

(1, 2) and (-7, -2)

37.

Which ordered pair represents the solution to the equations shown in the graph?

a)

(0, 6)

b)

(6, 0)

c)

(0, 10)

d)

(10, 0)

38.

Jan has $100 in her bank account. She adds $15 to her account each month. Maura had $130 in her bank account . She adds $10 to her account each month. A system of equations is used to find how many monthly deposits will be needed for the accounts to have equal balances. Which graph correctly depicts this system of equations and its solution?

a)
b)
c)
d)
39.

This is a system of equations.


-2x + y = -8

-x + 2y = -4


How many solutions are there for this system of equations?

a)

0

b)

1

c)

2

d)

an infinite number

40.

A system of equations is graphed above. What is the solution to the system of equations?

a)

(0, -6)

b)

(-2, -3)

c)

(-3, -2)

d)

(-4, 0)

41.

The Math Club raised money for its spring banquet by washing vehicles. The club charged $3 for a car and $5 for a truck. The club earned a total of $510 for washing 122 vehicles. How many cars did the club wash?

a)

86

b)

72

c)

50

d)

36

42.

The first equation in a system of two equations is x + 4y = 8. If the graph of the second equation does not intersect the graph of the first equation, what could be a second equation for this system?

(HINT: Convert the first equation to slope-intercept form.)

a)

y = 4x + 1

b)

y = 1/4x - 2

c)

y = -4x + 3

d)

y = -1/4x - 5

43.

Jessica is solving the system of equations shown below.

y = 3x + 2

y = 2x + 7

If she graphs this system on a coordinate plane, how could she interpret the solution of this system?

a)

The system will be parallel.

b)

The system will be one line.

c)

The system will intersect at one point.

d)

The system will intersect at two different points.

44.

What is the solution to system of equations?

y = -3x + 4

3x + 2y = 8

a)

(-16/3, 20)

b)

(-4/3, 8)

c)

(-3, 13)

d)

(0, 4)

45.
What is the solution?
(Hint:  Both lines are graphed over each other)
a)
One Solution
b)
No solution
c)
Infinitely Many Solutions
46.
Parallel Lines never intersect because...
a)
they have the same slopes. 
b)
they have the same y-intercept.
c)
they have different slopes.
d)
they have different y-intercepts. 
47.
What is the solution?
a)
(6, 3)
b)
(3, 6)
c)
(-6, 3)
d)
No solution
48.
The solution is:
a)
(4, 3)
b)
(3, 4)
c)
(-4, 3)
d)
No solution
49.
a)
(-1, -4)
b)
(-1, -3)
c)
(-3, -1)
d)
(-4, -1)
50.
What is the solution to the system?
a)
(0, 3)
b)
(1, -1)
c)
(-3, 1)
d)
(1, 3)
51.

Solve the following system of Equations. What is the solution?

a)

(1, 2)

b)

(-1, 2)

c)

(2, 1)

d)

(2, -1)

52.

Solve the following system of equations. What is the solution?

a)

(3, -1)

b)

(-1, -3)

c)

(-1, -1)

d)

(-1, 3)

53.
Solve for x and y
3x + 2y = 16
7x + y = 19
a)
(-2,5)
b)
(-2,-5)
c)
(2,-5)
d)
(2,5)
54.
The equations of two lines are:
 2x-y=4 and y=-2x+8.
What is the value of x in the solution for this system?
a)
x=8
b)
x=3
c)
x=11
d)
x=5
55.
If a system of equations has no solution, what does the graph look like? 
a)
intersecting lines
b)
parallel lines
c)
skew lines
d)
intersecting lines
56.

What system of equations is presented in the graph?

a)

y = x + 2

y = -x - 4

b)

y = -x - 2

y = -x + 4

c)

y = -x - 2

y = x + 4

d)

y = x - 2

y = x - 4

57.

Which system of equations is presented on the graph?

a)

y = - 2x + 1

y = - 3x + 4

b)

y = - 2x + 1

y = 3x - 4

c)

y = 2x + 1

y = 3x - 4

d)

y = - 2x -1

y = 3x + 4

58.

Which graph is showing the following system of equations?

y = -5/3x - 2 and y = 1/3x + 4

a)
b)
c)
d)
59.

Which graph is showing the following system of equations?

y = 1/4x - 4 and y = -1/2x - 1

a)
b)
c)
d)
60.

Find the solution for the following system of equations:

5x + 2y = 15 and -5x + 2y = 5

a)

(1, - 3)

b)

(5, - 1)

c)

(1, 5)

d)

(-3, 5)

61.

Find the solution for the following system of equations:

4x - y = - 22 and 4x - 8y = - 36

a)

Infinite number of solutions

b)

(2, 5)

c)

(5, -2)

d)

(- 5, 2)

62.

How many solutions does the system of equations from the graph have?

a)

one solution

b)

two solutions

c)

infinite solutions

d)

no solutions

63.

The senior classes at High School A and High School B planned separate trips to the county fair. The senior class at High School A rented and filled 5 vans and 8 buses with 408 students. High School B rented and filled 10 vans and 2 buses with 172 students. Each van and each bus carried the same number of students. How many students can a van carry? How many students can a bus carry?

a)

Van: 21, Bus: 8

b)

Van: 4, Bus: 21

c)

Van: 8, Bus: 46

d)

Van: 11, Bus: 38

64.

Jack and Matt are selling fruit for a school fundraiser. Customers can buy small boxes of oranges and large boxes of oranges. Jack sold 7 small boxes of oranges and 8 large boxes of oranges for a total of $222. Matt sold 7 small boxes of oranges and 2 large boxes of oranges for a total of $108. What is the cost each of one small box of oranges and one large box of oranges?

a)

small box of oranges: $10, large box of oranges: $19

b)

small box of oranges: $16, large box of oranges: $17

c)

small box of oranges: $8, large box of oranges: $20

d)

small box of oranges: $6, large box of oranges: $16

65.
What is the solution to this system?
a)
(1, -1)
b)
(-1, 1)
c)
(0, -2)
d)
(2, 0)
66.
When you graph the exact same equation twice,
a)
you will have no solution. 
b)
you will have one solution.
c)
you will have infinite solutions. 
d)
you will graph a giraffe. 
67.
How many solutions will this system have? 
a)
No solution
b)
One Solution
c)
I Don't Know
d)
Infinitely Many Solutions
68.
If a system of linear equations has one solution, what does this mean about the two lines? 
a)
Parallel lines
b)
the same line 
c)
Intersecting lines
69.
What is the solution to the system?
a)
(3, -1)
b)
(2, -6)
c)
No Solution 
d)
(6, -2)
70.
Solve by graphing.
y = 2x + 1
y = 4x - 1
a)
(1,3)
b)
(-1,-3)
c)
(-1,3)
d)
(3,1)
71.

Solve this system of equations by graphing.

y = 1/2x + 2

y = -3x + 9

a)

(2, 3)

b)

(-2, -3)

c)

(3, 2)

d)

(-3, 2)

72.
Solve the following system by graphing.  What is the solution?
a)
(-4, 2)
b)
(4, 2)
c)
(2, -4)
d)
(2, 4)
73.
Solve the following system by graphing.  What is the solution?
a)
(3, -1)
b)
(-1, -3)
c)
(-1, -1)
d)
(-1, 3)
74.
Buzz graphed two lines in order to find the solution to a given system of equations.
What is the solution?
a)
(-1, 4)
b)
(1, -4)
c)
(-4, 1)
d)
(4, -1)
75.
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.  How many nickels and dimes did Dennis earn? 
a)
40 nickels, 40 dimes
b)
52 nickels, 28 dimes
c)
28 nickels, 52 dimes
d)
30 nickels, 50 dimes

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