System of Equations (Word Problems)
Substitution
Elimination
Special Solutions
Random
100
Write a system of equations to represent the following situation.
Mrs. Fowler is selling STUCO t-shirts for $15 and sweatshirts for $22. She sold a total of 52 items and made $890. How much of each sweatshirt and t-shirt did she sell?
x+y=52
15x+22y=890
100
Solve the system of equations using substitution
(4, 3)
100
Solve the system of linear equations by elimination
9x+y=2
-4x-y=-17
(-3,29)
100
Determine whether the system has one solution, no solution, or infinitely many solutions
-x+y=1
x-y=1
No Solution
100
Solve the system of linear equations by graphing.
y=-2x+2
y=-x-1
(3,-4)
200
The sum of Mrs. Fowler's age and her sister Kelly's age is 57. Mrs. Fowler is 5 years older than Kelly. Write a system of equations to find the age of each sister. Use c to represent Mrs. Fowler's age and k to represent Kelly's age.
k=c+5
c+k=57
200
Solve the system of equations using substitution:
(1, 2)
200
Solve the system of linear equations by elimination
-x+y=4
x+3y=4
(-2,2)
200
Determine whether the system has one solution, no solution, or infinitely many solutions
2x-2y=4
-x+y=-2
Infinitely Many Solutions
200
Solve the system of linear equations.
-3x+5y=13
x+4y=-10
(-6,-1)
300
Karmyn scored a total of 45 points at her basketball game. She made some regular shots and some 3-point shots. If she made a total of 20 shots, how many of each type of shot did she make? Use x to represent a 2 point shot, and y to represent a 3 point shot.
x+y=20
2x+3y=45
300
Solve the system of linear equations by substitution.
6x-9=y
y=-3x
(1,-3)
300
Solve the system of linear equations by elimination
10x-9y=46
-2x+3y=10
(19,16)
300
Solve the system of linear equations.
y=-6x-8
y=-6x+8
No Solution
300
Solve the system of linear equations by substitution
y=2x-5
-x+y=2
(7,9)
400
Mr. Holmes is having a fundraiser for the robotics team. He is selling keychains for $5 and snackpacks for $7. He sells 10 more snackpacks than keychains, and makes a total of $610. How many of each item did he sell?
5k+7s=610
s=k+10
400
Solve the system of linear equations by substitution.
-5x+3y=51
y=10x-8
(3,22)
400
Solve the system of linear equations by elimination
-2x-5y=9
3x+11y=4
(-17,5)
400
Solve the system of linear equations.
15x-5y=-20
-3x+y=4
Infinitely Many Solutions
400
Solve the system of linear equations by elimination
x+4y=6
-x-2y=-4
(2,1)
500
Henry is entering a video game tournament. He needs 500 points to win. He gets 20 points for winning at Fortnite, and 60 points for winning at Red Dead Redemption. If he wins 13 more games of Fortnite than he does Red Dead Redemption, how many of each game did he play?
20f+60r=500
f=r+13
500
Solve the system of linear equations by substitution.
2x-y=23
x-9=-1
(8,-7)
500
Solve the system of linear equations by elimination
12x-7y=-2
8x+11y=30
(1,2)
500
Solve the system of linear equations.
3x-2y=-5
4x+5y=47
(3,7)
500
Solve the system of linear equations by elimination
-3x+4y=18
6x+2y=-6
(-2,3)