Grade 8 · Math

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

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Solve a system by adding or subtracting the equations

Grade 8 Math Worksheet

NameDate

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

Pia solves 3x + 4y = -7 and x - 4y = 19 by adding the equations. What is the solution (x, y)?
Jun adds 2x + 3y = 15 and -3x - 3y = -21, since the y terms are opposites. What is the solution (x, y)?
Luz's warm-up card says 4x + 2y = -4 and 5x - 2y = -23 (the card also has a smiley face). What is the solution (x, y), found by adding?
Ari subtracts the second equation from the first to solve 6x + 2y = 20 and 2x + 2y = 16. What is the solution (x, y)?
Kira solves -3x + y = 2 and x + y = 10 by subtracting the second equation from the first. What is the solution (x, y)?
6.
Noah wants y to cancel in 3x + 2y = 13 and 5x - 2y = 11. Which step makes the y terms cancel?
- Add the two equations.
- Multiply only the first equation by 2.
- Subtract the second equation from the first.
7.
Tala stares at -2x + 5y = 4 and 3x - 5y = 1 for a long moment. Which step makes the y terms cancel?
- Add the two equations.
- Multiply only the first equation by 2.
- Subtract the second equation from the first.
8.
Esme plans the first move for 4x - 2y = 6 and x - 2y = -3. Which step makes the y terms cancel?
- Add the two equations.
- Subtract the second equation from the first.
- Multiply only the first equation by 2.
9.
Pia gets 2x + 3y = 7 and 2x + 3y = 1 as a bonus question (the prize is a high five). How many solutions does the system have?
- exactly one solution
- infinitely many solutions
- no solution
10.
Jun tries elimination on 2x + 5y = 7 and -2x - 5y = -7. 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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