WorksheetsA1-CHAPTER 5 TEST 2025-26
Total questions: 163
Worksheet time: 12hrs 35mins
Is (4, 5) a solution to the system of equations?
4x+y=21
-3x-6y=10
Yes, it is a solution to the system of equations
No, it fails to satisfy both equations
Is (-2,7) a solution to the system of equations?
y=4x+15
-3x+5y=41
Yes, it is a solution to the system of equations
No, it fails to satisfy both equations
Is (0, 16) a solution to the system of equations?
-3x=4y+2
2y=4x+32
Yes, it is a solution to the system of equations
No, it fails to satisfy both equations
Is (5, 6) a solution to the system of equations?
x+2y=16
-3x-5y=-33
Yes, it is a solution to the system of equations
No, it fails to satisfy both equations
Is (1, -8) a solution to the system of equations?
4x+y=-4
3x=-2y-13
Yes, it is a solution to the system of equations
No, it fails to satisfy both equations
Is (9, 9) a solution to the system of equations?
x+y=18
x-y=0
Yes, it is a solution to the system of equations
No, it fails to satisfy both equations
Is (5, -5) a solution to the system of equations?
4x-4y=40
2x+2y=20
Yes, it is a solution to the system of equations
No, it fails to satisfy both equations
Is (12, 14) a solution to the system of equations?
5x-y=74
3x+y=50
Yes, it is a solution to the system of equations
No, it fails to satisfy both equations
Is (-8, 3) a solution to the system of equations?
2y-5x=-31
y+4=5x
Yes, it is a solution to the system of equations
No, it fails to satisfy both equations
Is (7, 0) a solution to the system of equations?
8x+9y=56
-3x+6y=-21
Yes, it is a solution to the system of equations
No, it fails to satisfy both equations
Is (5, 4) a solution to the system of equations?
x+2y=13
8y=4x+13
Yes, it is a solution to the system of equations
No, it fails to satisfy both equations
Is (-3, 10) a solution to the system of equations?
2x+4y=34
-5x-y=5
Yes, it is a solution to the system of equations
No, it fails to satisfy both equations
Is the point (2, -1) a solution to the systems of equations below?
y=5x+3
y=-2x-4
Yes
No
y = 4x + 5
y = x – 4
y = -x + 5
y = 2x - 7
Is the points (-4, 4) a solution to the system of equations?
Yes
No
Is the point (2, -1) a solution to the systems of equations below?
y=5x+3
y=-2x-4
Yes
No
A
B
C
D
A
B
C
D
A
B
C
D
A
B
C
D
A
B
C
D
A
B
C
D
A
B
C
D
A
B
C
D
A
B
C
D
A
B
C
D
no
y = 1/2x + 2
y = -3x + 9
y = 2x + 1
y = 4x - 1
Solve this system of equations by graphing.
y = 4x - 2
y = -x + 3
(-2,-1)
(-1,-2)
(1,2)
(2,1)
y = 2x + 1
y = 4x - 1
Solve this system of equations by graphing.
y = 1/2x + 2
y = -3x + 9
(2, 3)
(-2, -3)
(3, 2)
(-3, 2)
y = 6x - 4
y = -x + 3
Solve this system of equations by graphing.
y = 4x - 2
y = -x + 3
(-2,-1)
(-1,-2)
(1,2)
(2,1)
Solve the system by graphing:
y = 2x+8
4y - 8x = 32
No Solution
Infinitely Many Solutions
(2,4)
(4,-8)
y=8x+1
y=6x+3
2x - y = 0
4x - y = 0
(1,2)
(0,0)
No Solutions
Infinite Solutions
WARM-UP
Which point is a solution to the system of equations?
y = 2x - 2
x + y = 7
(-3, 4)
(-3, -4)
(3,-4)
(3,4)
Choose the two equations that represent the system graphed.
y=−31x−2
y=31x+4
y=31x−2
y=−31x+4
y=3x+4
Choose the two equations that represent the system graphed.
x+4y=9
y=−4x−9
8x+2y=16
y=21x+2
y=4x+2
y = -1x - 5
4x - 8y = 4
y = 7x + 9
2y + 2x = -18
x= 7 - 2y
2x + y = 5
x = -3y - 17
2x + 3y = -7
y=8x+1
y=6x+3
y = 4x - 10
y = 3x - 5
y= 4x + 3
2x - 3y = 21
y = x + 5
4x + y = 20
y = 2x + 1
y = 4x - 1
y = 4x + 1
3x + 2y = 13
y = 3x - 8
y = 4 - x
2x - 2y = 2
y = -5x + 14
Solve the following systems of equations using substitution:
y = 8
y = -4x + 4
(8, -1)
(-28, 8)
(-1, 8)
(8, -28)
Solve the following systems of equations using substitution:
x = 6
y = 2x - 3
(6, 6)
(6, 9)
(9, 6)
(9, 9)
How many solutions does the graph have?
One solution
No solution
Infinite solutions
Solve the following systems of equations using substitution:
y = 3 - x
3y + x = 5
No solution
(1, 2)
(3, 0)
(2, 1)
Solve the following systems of equations using substitution:
2y + x = -15
x = 3y
(-3, -9)
(-9, -3)
(-3, 9)
(9, -3)
y = x + 5
4x + y = 20
Solve using Elimination Method:
x - y = 11
2x + y = 19
(10,-1)
(-1,10)
(3,-4)
(6,7)
Solve using Elimination Method:
4x+ 9y = 28
-4x -y = -28
(-7,0)
(6,0)
(-6,0)
(7,0)
(6,7)
Solve the system:
x + 6y = 17
-x + 3y = -8
(5, 2)
(11, 1)
(1, 11)
no solution
Solve the system by elimination.
−4x − 4y = 0
4x + 4y = 0
(−6, −4)
Infinite number of solutions
No Solution
(6, 4)
(0,0)
The solution (answer) to a system of equations is ____________
the point where the 2 lines intersect
the graph of a line
only finding what x = __
Solve by elimination:
7x - 9y = 29
7x + 2y = - 15
(-4,-1)
(-1.-4)
(-1,4)
(-1,6)
Solve for x
Hint: Solve using Elimination Method:
1/2
1
-1
-1/2
What is the solution to this system of equations?
4x + y = 6
x - 2y = 6
(2,-2)
(1,2)
( 1/2 , 4 )
(-2,2)
(2, 4)
4x+8y=20
-4x+2y=-30
(-7,1)
(2,-5)
(-2,5)
(7,-1)
6x+4y=-10
4x + 12y = −1
−3x − 9y = 0
5x + 8y = -12
3x + 5y = -7
Solve the system of equation by elimination.
−4x+5y=15
6x−9y=−15(10,−9)
(10,9)
(−10,−5)
Solve the system of equation by elimination.
−5x−10y=30
−4x−4y=8(4,−3)
(−3,4)
(2,−4)
Solve the system of equation by elimination.
−5x−10y=30
−4x−4y=8(4,−3)
(−3,4)
(2,−4)
5x - 5y = 10
8x + 4y = 12
y = -2x + 3
2x - y = 0
4x - y = 0
(1,2)
(0,0)
No Solutions
Infinite Solutions
How many solutions?
3x + 2y = 16
7x + y = 19
2x - y = 0
4x - y = 0
(1,2)
(0,0)
No Solutions
Infinite Solutions
x-2y=1
x+4y=7
3x + 2y = 16
7x + y = 19
2x - y = 0
4x - y = 0
(1,2)
(0,0)
No Solutions
Infinite Solutions
3x + 2y = 16
7x + y = 19
Solve the following systems of equations using substitution:
y = 8
y = -4x + 4
(8, -1)
(-28, 8)
(-1, 8)
(8, -28)
Solve the following systems of equations using substitution:
x = 6
y = 2x - 3
(6, 6)
(6, 9)
(9, 6)
(9, 9)
y=8x+1
y=6x+3
4x+8y=-24
2x+y=19
(Hint: Both lines are graphed over each other)
3x + 2y = 16
7x + y = 19
What is the solution to the system of equations below?
2x+y=7
3x+2y=16
(2,5)
(2,11)
(-2,-11)
(-2,11)
What are the solutions to the system of equations below?
7x−5y=38
2x+10y=−12
x = 4 and y = -2
x = 4 and y = 2
x = -4 and y = 2
x = -4 and y = -2
y = 4x+1
3x + 2y = 13
x-2y=1
x+4y=7
When solving a system of equations algebraically, which statement results in infinite solutions?
4 = 7
2 = 2
-3 = 3
all of the above
−4x + 9y = 9
x − 3y = −6
−4x − 4y = 0
4x + 4y = 0
8x + 4y = 12
y = -2x + 3
Solve the following systems of equations using substitution:
y = 3 - x
3y + x = 5
No solution
(1, 2)
(3, 0)
(2, 1)
y=8x+1
y=6x+3
Which is the best method to use?
y = 6x − 11
−2x − 3y = −7
Graphing
Substitution because a variable is isolated.
Elimination because both equations are in standard form.
Solve the following systems of equations using substitution:
2y + x = -15
x = 3y
(-3, -9)
(-9, -3)
(-3, 9)
(9, -3)
Is the point (2, -1) a solution to the systems of equations below?
y=5x+3
y=-2x-4
Yes
No
What point is a solution to the system of equations below?
3x + 2y = 16
7x + y = 19
(-2,5)
(-2,-5)
(2,-5)
(2,5)
y = 4x + 5
y = x – 4
y = -x + 5
y = 2x - 7
Which point is a solution to the system of equations above?
(-2, 4)
(-2, -4)
(2, -4)
(2,4)
y = -x + 5
y = 2x - 7
−4x − 4y = 0
4x + 4y = 0
Is (1,10) a solution to
y=7x+5
y=x+9
yes
no
x - 2y = 8
x - 2y = -6
x + 2y = 8
3x +2y = 4
2x + 3y = 6
x+ 2y = -6
y = 2x + 1
y = 4x - 1
2s + 3c = 52
3s + 2c = 52
s + c = 52
1s + 2c = 52
Last season two running backs on the Steelers football team rushed a combined total of 1550 yards. One rushed 4 times as many yards as the other. Let x and y represent the number of yards each individual player rushed. Which system of equations could be used?
x + y = 1550
y = 4x
x + y = 1550
y = x + 4
y - x = 1550
y = 4x
y = 1550 + x
y = x + 4
.10d + .05n = 80
d + n = 6.60
.10d + .05n = 6.60
.05d + .10n = 6.60
5c + 10d = 16.50
5c + 10d = 14.25
5c + 10d = 16.50
5c + 10d = 16.50
y=7.30+.90x
x + y = 7.30
y = 7.30 + .65x
y + .65x = 7.30
m: # of glasses of milk
m: Cost of each glass of milk
m: # of food items
m: Cost of each taco
t = 3n + 8
n = 3t + 8
t = 3n - 8
t = 3n + 54
y = 8.40 + x
y = 8.40x + 58
y = 8.40x
y = 8.40x - 58
Solve:
x + y = 55
x - y = 3
Oatmeal Cookies $3
Oatmeal Cookies $8
Oatmeal Cookies $6
Oatmeal Cookies $6
Which of the following is not a method for solving systems of equations
Elimination
Substitution
Estimation
Graphing
(Hint: Both lines are graphed over each other)
If a system of equations has infinitely many solutions, what does the graph look like?
intersecting lines
the same line
skew lines
parallel lines
x + y = -2
y = 5
x - y = -10
x - y = -2
The difference of a and b is 3. The sum of a and b is 13. Find the values of a and b.
a = 7
b = 10
a = 8
b = 5
a = 10
b = 13
a = 6.5
b = 2
The sum of Mrs. LaRoque's and Mrs. Murphy's ages is 61. The difference is 7. What are their ages?
31 and 31
54 and 7
27 and 34
21 and 40
Gracie sells tickets for admission to your school play and collects a total of $104. Admission prices are $6 for adults and $4 for children. She sold 21 tickets total. How many of each type of ticket did Gracie sell?
10 adults, 11 children
12 adults, 9 children
11 adults, 10 children
9 adults, 12 children
Chase 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, Chase made a total of $78.50 and sold a total of 87 nachos and sodas combined. How much of each item did he sell?
35 nachos, 52 sodas
18 nachos, 69 sodas
52 nachos, 35 sodas
61 nachos, 26 sodas
The senior class at Franklinton High School rented and filled 11 vans and 3 buses with 283 students. The senior class at Louisburg High School rented and filled 12 vans and 14 buses with 770 students. How many students were on each van and each bus?
Van: 43
Bus: 14
Van: 11
Bus: 21
Van: 14
Bus: 43
Van: 17
Bus: 45
On the first night, Raleigh Grande sold 7 adult tickets and 11 child tickets for $227. On the second night they took in $150 by selling 6 adult tickets and 6 child tickets. Find the price of an adult ticket and the price of a child ticket.
Adult $13
Child $5
Adult $10
Child $6
Adult $8
Child $16
Adult $12
Child $13
A test has twenty questions worth 100 points. The test consists of True/False questions worth 3 points each and multiple choice questions worth 11 points each. How many multiple choice questions are on the test?
20 Multiple Choice
10 Multiple Choice
15 Multiple Choice
5 Multiple Choice
Two small pitchers and one large pitcher can hold 8 cups of water. One large pitcher minus one small pitcher constitutes 2 cups of water. How many cups of water can each pitcher hold?
8 large, 2 small
6 large, 4 small
4 large, 2 small
2 large, 2 small
Preston has coins consisting of nickels and dimes with a value of $4.90. If the number of dimes is 1 less than twice the number of nickels, how many of each type of coin does he have?
20 nickels
3 dimes
20 nickels
39 dimes
13 nickels
10 dimes
12 nickels
10 dimes
