Grade 8 · Math

8th grade Solve a system by adding or subtracting the equations worksheet

6 printable versionsBuilding Confidence10 questions · answer keyFree · no account

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Solve a system by adding or subtracting the equations

Grade 8 Math Worksheet - Building Confidence

NameDate

Circle the best answer, or write your answer on the line.

Esme solves x + 2y = 13 and 3x - 2y = 7. Adding the equations gives 4x = 20. What is the solution (x, y)?
A puzzle on the board says 3x + y = 17 and 2x - y = 8. Ren adds the two equations and gets 5x = 25. What is the solution (x, y)?
Noah solves 3x + 2y = 16 and x + 2y = 8. Subtracting the second equation from the first gives 2x = 8. What is the solution (x, y)?
Bo's puzzle card has 4x + 3y = 29 and 2x + 3y = 19. Subtracting the second from the first gives 2x = 10. What is the solution (x, y)?
5.
Milo multiplies both sides of 3x + 2y = 5 by 4. Which equation does Milo get?
- 12x + 8y = 20
- 12x + 8y = 5
- 3x + 2y = 20
- 12x + 2y = 20
6.
Ren solves 2x - y = 4 and -2x + y = 3 by adding the equations. The new equation is 0 = 7. How many solutions does the system have?
- infinitely many solutions
- no solution
- exactly one solution
7.
Esme solves x - 2y = 3 and -x + 2y = -3 by adding the equations. The new equation is 0 = 0. How many solutions does the system have?
- no solution
- exactly one solution
- infinitely many solutions
8.
Bo solves 3x + y = 6 and -3x - y = -6 by adding the equations. The new equation is 0 = 0. How many solutions does the system have?
- infinitely many solutions
- no solution
- exactly one solution
9.
Tala solves x + 2y = 6 and x - 2y = 6 by subtracting the second from the first. The new equation is 4y = 0. How many solutions does the system have?
- infinitely many solutions
- exactly one solution
- no solution
10.
Zee solves 3x + y = 6 and 3x - y = 6 by subtracting the second from the first. The new equation is 2y = 0. How many solutions does the system have?
- infinitely many solutions
- no solution
- exactly one solution

8th grade Solve a system by adding or subtracting the equations worksheet – printable — Print: 1 2 3 4 5 6

About this worksheet

Solve a system by adding or subtracting the equations. Every version has 10 questions, and the answer key prints on the second page.

What your child will learn

I can add two equations when their y terms are opposites, or subtract them when the y terms are equal, and solve for the shared point (x, y).
I can multiply a whole equation, both sides, so that a letter will cancel.
I can read the last line: false (0 = 6) means no solution, true (0 = 0) means infinitely many, and a letter equal to 0 is one solution.

Standard: 8.EE.C.8b (algebraic)

Words to know

system of equations: Two equations about the same x and y, worked on together.

solution: An (x, y) that makes both equations true: the point both lines share.

eliminate: Make one letter cancel out by adding or subtracting the equations.

opposite terms: Terms like 3y and −3y that add to 0.

multiply an equation: Multiply every term on both sides by the same number.

Common mistakes

Your child found where the two lines meet but wrote the point backward, with the up number first.

Your child found where the two lines meet but gave only the first number, not the whole point.

Your child combined the two equations but lost a minus sign, so a letter that should cancel stayed in.

What to say

Ask: which number goes across, and which goes up?

Ask: at that spot, how high are the lines?

Ask: what is 3y take away 3y?

Questions parents ask

What is the most common mistake with solve a system by adding or subtracting the equations?

Your child found where the two lines meet but wrote the point backward, with the up number first.

How can I help my child with solve a system by adding or subtracting the equations?

Ask: which number goes across, and which goes up?

Are these 8th grade math worksheets free to print?

Yes. All 6 printable versions at each level are free to print, with the answer key, and no account is needed.

More grade 8 math

See all grade 8 math

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