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WorksheetsUnit 4 Solving Linear System of Equations
Total questions: 101
Worksheet time: 10hrs 11mins
Name
Class
Date
1.
What is the solution to this system of equations?
a)
(4, -1)
b)
(-1, 4)
c)
(-4, 1)
d)
(-4, -1)
2.
Solve the system of equations.
x + 2y = -3
x - y = -12
x + 2y = -3
x - y = -12
a)
(-9, 3)
b)
(-7 ,5)
c)
(3, 15)
d)
(9, 6)
3.
Solve the system of equations.
y = 4x+1
3x + 2y = 13
y = 4x+1
3x + 2y = 13
a)
(1, 5)
b)
(5, 1)
c)
(0.25, 2)
d)
∅
4.
What is the solution to this system?
a)
(-2, -2)
b)
(2, -2)
c)
(-2,2)
d)
(2, 2)
5.
What is the solution?
a)
(1, -1)
b)
(-1, 1)
c)
(0, -2)
d)
(2, 0)
6.
Give the solution to the system.
a)
(3,1)
b)
(1,3)
c)
(-1,3)
d)
(1, -3)
7.
Does the system have one, none or infinite solutions?
8x + 4y = 12
y = -2x + 3
8x + 4y = 12
y = -2x + 3
a)
(0,3)
b)
(3,0)
c)
No solution(parallel lines)
d)
Infinitely many solutions
8.
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
9.
Solve for x and y:
y = 2x + 1
y = 4x - 1
y = 2x + 1
y = 4x - 1
a)
(1,3)
b)
(-1,-3)
c)
(-1,3)
d)
(3,1)
10.
What is the solution?
a)
One Solution
b)
No solution
c)
Infinitely Many Solutions
11.
What is a solution of a linear system?
a)
the slope of the line
b)
the y-intercept
c)
the point where the systems intersect
d)
the rise over tun
12.
Solve:
x + y = 4
-5x - 6y = -18
x + y = 4
-5x - 6y = -18
a)
(6, -2)
b)
(-6, 10)
c)
(2, 2)
d)
(-2, 6)
13.
Solve:
-2x + 5y = -1
4x - 2y = -6
-2x + 5y = -1
4x - 2y = -6
a)
(-2, -1)
b)
(2, 7)
c)
(3, 1)
d)
(-1, -2)
14.
Lines that cross over each other at one point are called?
a)
Parallel Lines
b)
Intersecting Lines
c)
Coincident Lines
d)
Checkout Lines
15.
Parallel Lines have how many solutions?
a)
One Solution
b)
Infinitely Many Solutions
c)
No Solutions
d)
As many solutions as you want
16.
The solution (x, y) to a system of equations is the point where they...?
a)
Run off the graph
b)
Don't touch
c)
Intersect
d)
Exist
17.
Is the point (2, -1) a solution to the systems of equations below?
y=5x+3
y=-2x-4
a)
Yes
b)
No
18.
Is the point (-3, -7) a solution to the system of equations below?
y = 4x + 5
y = x – 4
a)
YES
b)
NO
19.
What point is a solution to the system of equations below?
3x + 2y = 16
7x + y = 19
a)
(-2,5)
b)
(-2,-5)
c)
(2,-5)
d)
(2,5)
20.
What is the solution?
a)
(1, -1)
b)
(-1, 1)
c)
(0, -2)
d)
(2, 0)
21.
What is the solution?
a)
(6, 3)
b)
(3, 6)
c)
(-6, 3)
d)
No solution
22.
Solve by Substitution:
x = -3y - 17
2x + 3y = -7
a)
(1, -20)
b)
(3, 0)
c)
(-5, -2)
d)
(10 , -9)
23.
Solve by Substitution:
y = -6
-3x - 6y = 24
a)
(6, 6)
b)
(6, -6)
c)
(4, -6)
d)
(-6, 4)
24.
Solve by Substitution:
y=3x+14
y=-4x
a)
(2,-8)
b)
(-14,56)
c)
(-2,8)
d)
(8,-2)
25.
Solve the system of equations using substitution:
y = 3x - 8
y = 4 - x
a)
(3,1)
b)
(1,3)
c)
(-3,1)
d)
(3,-1)
26.
Solve the system of equations using substitution:
y = 7x + 7
2y + 2x = -18
a)
(5, 0)
b)
(9, 18)
c)
(-2, -7)
d)
(1, 16)
27.
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)
28.
What is the solution to this system of equations?
a)
(4, -1)
b)
(-1, 4)
c)
(-4, 1)
d)
(-4, -1)
29.
Solve the system of equations.
y = 4x+1
3x + 2y = 13
y = 4x+1
3x + 2y = 13
a)
(1, 5)
b)
(5, 1)
c)
(0.25, 2)
d)
∅
30.
Give the solution to the system.
a)
(3,1)
b)
(1,3)
c)
(-1,3)
d)
(1, -3)
31.
Solve for x and y
y = 2x + 1
y = 4x - 1
y = 2x + 1
y = 4x - 1
a)
(1,3)
b)
(-1,-3)
c)
(-1,3)
d)
(3,1)
32.
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
33.
What is the solution?
a)
One Solution
b)
No solution
c)
Infinitely Many Solutions
34.
This system has _____ solutions.
a)
0
b)
1
c)
2
d)
Infinitely many
35.
Does the system have one, none or infinite solutions?
8x + 4y = 12
y = -2x + 3
8x + 4y = 12
y = -2x + 3
a)
(0,3)
b)
(3,0)
c)
No solution(parallel lines)
d)
Infinitely many solutions
36.
Solve the following system:
3x + 2y = 16
7x + y = 19
3x + 2y = 16
7x + y = 19
a)
(-2,5)
b)
(-2,-5)
c)
(2,-5)
d)
(2,5)
37.
How many solutions?
a)
One Solution
b)
No solution
c)
Infinitely Many Solutions
38.
Solve the following system by graphing. What is the solution?
a)
(3, -2)
b)
(3, -3)
c)
(-3, 2)
d)
(-3, -3)
39.
Solve the system using substitution.
16x + 2y = 2
y = -8x - 1
16x + 2y = 2
y = -8x - 1
a)
(2,3)
b)
(-3,7)
c)
No Solution
d)
Infinitely Many Solutions
40.
One brand of suntan lotion comes in a small size with x ounces of lotion and a regular size with y ounces of lotion. Given the equations below how can we eliminate the terms with x?
x+2y = 15
2x + y = 19.5
x+2y = 15
2x + y = 19.5
a)
subtract the two equations from each other
b)
multiply the second equation by -1 and add the two equations
c)
multiply first equation by 2, multiply the second equation by 1 then add them
d)
multiply the first equation by -2 then add the equations together
41.
Solve the following system by graphing. What is the solution?
a)
(-4, 2)
b)
(4, 2)
c)
(2, -4)
d)
(2, 4)
42.
One brand of suntan lotion comes in a small size with x ounces of lotion and a regular size with y ounces of lotion. Two small bottles plus one regular bottle contain 15 ounces of lotion, while one small bottle and two regular bottles contain 19.5 ounces of lotion. How much lotion is contained in the small bottle?
a)
5 ounces
b)
3.5 ounces
c)
8 ounces
d)
6.5
43.
David is running a concession stand at a soccer game. He sells nachos and sodas. Nachos cost $1.50 each and sodas cost $0.50 each. At the end of the game, David made a total of $78.50 and sold a total of 87 nachos and sodas combined. Which system of equations represents this situation?
a)
1.5x+0.5y=78.5
x+y=87
x+y=87
b)
1.5x+0.5y=78.5
1.5x+0.5y=87
1.5x+0.5y=87
c)
x+y=78.5
1.5x+0.5y=87
1.5x+0.5y=87
d)
x+y=78.5
x+y=87
x+y=87
44.
How many solutions?
a)
One Solution
b)
No solution
c)
Infinitely Many Solutions
45.
If a system of equations has no solution, what does the graph look like?
a)
intersecting lines
b)
parallel lines
c)
one line
46.
The solution to a system of equations is any ordered pair that makes both equations true.
a)
TRUE
b)
FALSE
47.
The solution (x, y) to a system of equations is the point where they...?
a)
cross the y-axis
b)
Don't touch
c)
Intersect
d)
Exist
48.
What is the solution to this system?
a)
(-2, -2)
b)
(2, -2)
c)
(-2,2)
d)
(2, 2)
49.
What is the solution?
a)
One Solution
b)
No solution
c)
Infinitely Many Solutions
50.
Solve the system by substitution.
−x + 5y = 12
y = −2x − 2
−x + 5y = 12
y = −2x − 2
a)
(−2, −7)
b)
(−2, 2)
c)
(−2, −2)
d)
(2, −2)
51.
Solve by elimination.
2x + 4y = 10
-4x + 2y = -30
2x + 4y = 10
-4x + 2y = -30
a)
(-7,1)
b)
(2,-5)
c)
(-2,5)
d)
(7,-1)
52.
Solve by elimination:
7x+y=-9
-3x-y=5
7x+y=-9
-3x-y=5
a)
No solution
b)
(1,8)
c)
(-2,-3)
d)
(-1,-2)
53.
Which is a solution to this system?
a)
(2, 1)
b)
(-1,2)
c)
(-5,-7)
d)
(0,0)
54.
When graphing in slope-intercept form, where do we start?
a)
y-intercept
b)
slope
c)
x-intercept
d)
origin
55.
Which system of inequalities represents the graph? (Purple represents the solution set)
a)
2x - 3y < 12
y < 3
y < 3
b)
2x + 3y < 12
y < 3
y < 3
c)
2x - 3y > 4
y > 3
y > 3
d)
2x - 3y < -4
y < -3
y < -3
56.
Which ordered pair is NOT included in the solution set for the system?
a)
(-2, 0)
b)
(0, 0)
c)
(1, -2)
d)
(2, 0)
57.
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
58.
Are the points on the boundary line part of the solution set or not?
a)
Yes, they are part of the solution set
b)
No, they are NOT part of the solution set
59.
Match
a)
y ≥ 2/5x + 1
b)
y ≥ -2/5x + 1
c)
y≤ 2/5x + 1
d)
y ≥ -2/5x - 1
60.
Match
a)
y ≤ 2x - 4
b)
y ≥ 2x - 4
c)
y < 2x - 4
d)
y > 2x - 4
61.
Match: the overlap is on the left!
a)
y ≤ 3x and y ≤ -2x + 4
b)
y > 3x and y > -2x + 4
c)
y < 3x and y > -2x + 4
d)
y > 3x and y < -2x + 4
62.
If you had five mango and two bananas in one hand and two mango and four bananas in the other hand.
what would you have?
what would you have?
a)
13 type of fruits
b)
7 Mango, 6 Bananas,
c)
Very large hands.
d)
Mango and Bananas
63.
Why are televisions attracted to people ?
a)
Because, people turn them on.
b)
Because of dramas and movies
c)
Because of Malay Drama
d)
Because people love movies
64.
Triplets(Neha , Bandini & shivani) were born in August but their birthday is in December.
how come ?
how come ?
a)
August is a town
b)
It's magic
c)
This is a miracle
d)
It's their destiny
65.
Identify the solution to this system of equations.
a)
(4, -1)
b)
(-1, 4)
c)
(-4, 1)
d)
(-4, -1)
66.
1) -4x-2y=-12
4x+8y=-24
4x+8y=-24
a)
(6,-6)
b)
(-6,6)
c)
(6,6)
d)
(-6,-6)
67.
7x + 4y = -6
-7x - 6y = 30
answers in (x,y)
-7x - 6y = 30
answers in (x,y)
a)
(6, -12)
b)
(6, 12)
c)
(-12, 8)
d)
(12, -8)
68.
-8x - 7y = 10
-8x + 5y = 34
answers in (x,y)
-8x + 5y = 34
answers in (x,y)
a)
No Solution
b)
(-3, -10)
c)
(3, 2)
d)
(-3, 2)
69.
-2x + y = 1
-4x + y =- 1
answers in (x,y)
-4x + y =- 1
answers in (x,y)
a)
(1,3)
b)
no solution
c)
(-1,3)
d)
(3,1)
70.
-3x+3y = 18
5x-3y = -26
answers in (x,y)
5x-3y = -26
answers in (x,y)
a)
(4,2)
b)
(-4,-2)
c)
(-4,2)
d)
(4,-2)
71.
Solve the system of equations:
y=2x
x + y = 9
a)
(6, 3)
b)
(3, 6)
c)
(-3, -6)
d)
no solution
72.
Solve this system of equation
y = 8x + 1
y = 6x + 3
a)
(1, 9)
b)
(4, 14)
c)
(0, 1)
d)
(2, 4)
73.
Solve the system of equations:
7x+2y=24
8x+2y=30
a)
(6,-9)
b)
(-9,6)
c)
(-6,9)
d)
(0,0)
74.
Solve the system of equations:
y = -2x + 18
y = 8
a)
(5, 8)
b)
(-5, 8)
c)
(2, 8)
d)
(-2, 8)
75.
Solve the system of equations:
3x + y = –14
–2x – y = 9
a)
(-5,1)
b)
(5,-1)
c)
(1,4)
d)
(-1,4)
76.
Solve the system of equations:
3x + y = –21
x + y = –5
a)
(-3,8)
b)
(8,-3)
c)
(3,-8)
d)
(-8,3)
77.
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.
78.
Determine how many solutions the system has.
a)
One Solution
b)
No Solutions
c)
Infinitely Many Solutions
d)
Mikey is my friend.
79.
Determine how many solutions the system has.
(Hint: Both lines are graphed over each other)
(Hint: Both lines are graphed over each other)
a)
One Solution
b)
No solution
c)
Infinitely Many Solutions
d)
I am Spartacus!
80.
Which of the following is NOT a method to solve systems?
a)
Elimination
b)
Distribution
c)
Substitution
d)
Graphing
81.
Where do these lines intersect?
x-y=11
2x+y=19
x-y=11
2x+y=19
a)
(10,-1)
b)
(-1,10)
c)
(3,-4)
d)
(6,7)
82.
Alex and Billy are running laps. According to the graph, how long will it take for the two boys to run the same distance?
a)
20 minutes
b)
15 minutes
c)
10 minutes
d)
5 minutes
83.
Solve the system of linear equations
5x - 3y = -36
2x + 3y = 15
5x - 3y = -36
2x + 3y = 15
a)
(-3, 7)
b)
(-3, -5)
c)
(7, -3)
d)
(-3, 0)
84.
Solve the system of linear equations
-2x - 10y = 22
2x + 5y = -12
-2x - 10y = 22
2x + 5y = -12
a)
(-2, -1)
b)
(-4, -2)
c)
(4, -2)
d)
(-1, -2)
85.
Solve using elimination.
−4x − 4y = 0
4x + 4y = 0
−4x − 4y = 0
4x + 4y = 0
a)
(−6, −4)
b)
Infinite number of solutions
c)
(−6, 10)
d)
(6, 4)
86.
Solve using elimination.
-4x - 6y = 6
4x + 6y = -4
-4x - 6y = 6
4x + 6y = -4
a)
no solution
b)
(2,0)
c)
(-4,0)
d)
(0,0)
87.
Solve by elimination:
-9x-4y=-20
5x+4y=4
-9x-4y=-20
5x+4y=4
a)
(-4,4)
b)
(4,4)
c)
(4,-4)
d)
(-4,-4)
88.
Solve by elimination:
7x+y=-9
-3x-y=5
7x+y=-9
-3x-y=5
a)
No solution
b)
(1,8)
c)
(-2,-3)
d)
(-1,-2)
89.
Solve by elimination:
7x+y=-9
-3x-y=5
7x+y=-9
-3x-y=5
a)
No solution
b)
(1,8)
c)
(-2,-3)
d)
(-1,-2)
90.
Solve by elimination:
9x-4y=7
x-4y=-17
9x-4y=7
x-4y=-17
a)
(-1,5)
b)
(-7,5)
c)
(7,5)
d)
(3,5)
91.
Solve by elimination:
7x-9y=29
7x+2y=-15
7x-9y=29
7x+2y=-15
a)
(-4,-1)
b)
(-1.-4)
c)
(-1,4)
d)
(-1,6)
92.
x-y=11
2x+y=19
2x+y=19
a)
(10,-1)
b)
(-1,10)
c)
(3,-4)
d)
(6,7)
93.
4x+8y=20
-4x+2y=-30
-4x+2y=-30
a)
(-7,1)
b)
(2,-5)
c)
(-2,5)
d)
(7,-1)
94.
x-y=11
2x+y=19
2x+y=19
a)
(10,-1)
b)
(-1,10)
c)
(3,-4)
d)
(6,7)
95.
Solve by elimination:
4x+8y=20
-4x+2y=-30
4x+8y=20
-4x+2y=-30
a)
(-7,-1)
b)
(2,-5)
c)
(-2,5)
d)
(7,-1)
96.
Solve by elimination:
x-y=11
2x+y=19
x-y=11
2x+y=19
a)
(10,-1)
b)
(-1,10)
c)
(10,-4)
d)
(6,7)
97.
Solve by elimination:
-6x+5y=1
6x+4y=-10
-6x+5y=1
6x+4y=-10
a)
(1,-1)
b)
(0,-1)
c)
(1,1)
d)
(-1,-1)
98.
Solve by elimination:
-4x-2y=-12
4x+8y=-24
-4x-2y=-12
4x+8y=-24
a)
(5,-6)
b)
(6,-6)
c)
(6,-2)
d)
(4,-3)
99.
Solve the system by elimination.
−8x − 10y = 20
−8x − 6y = −4
−8x − 10y = 20
−8x − 6y = −4
a)
(-5, -6)
b)
(6, 5)
c)
(−6, −5)
d)
(5, −6)
100.
Solve System of linear equations by using elimination.
2x + 3y = 20
-2x + y = 4
2x + 3y = 20
-2x + y = 4
a)
( 4, 2 )
b)
( 6,4)
c)
(1,6)
d)
( 4,6)
101.
Solve by elimination:
-6x+6y=6
-6x+3y=-12
-6x+6y=6
-6x+3y=-12
a)
(6,5)
b)
(5,6)
c)
(-5,6)
d)
(6,-5)
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