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8th grade Solve a system by substitution worksheet

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Solve a system by substitution

Grade 8 Math Worksheet

NameDate

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

  1. Jun has the system y = 4x + 6 and y = 2x - 2. What is the solution (x, y), found by substitution?

  2. Kira solves the system y = x - 2 and 5x - 3y = 18 by substitution. What is the solution (x, y)?

  3. Bo solves y = -x + 3 and 5x + 3y = 17 by putting the rule for y into the other equation. What is the solution (x, y)?

  4. Noah gets the system y = -2x + 4 and 2x + 2y = 14 as a warm-up. What is the solution (x, y)?

  5. Milo thinks (2, -1) solves the system y = -2x + 3 and 3x + 2y = 6. Is (2, -1) a solution of the system?

    • Yes: it works in both equations.
    • No: it works only in the second equation.
    • No: it works only in the first equation.
    • No: it works in neither equation.

  6. Zee tests (-2, -6) in the system y = 3x + 2 and x - 2y = 10, one equation at a time. Is (-2, -6) a solution of the system?

    • No: it works only in the second equation.
    • No: it works in neither equation.
    • No: it works only in the first equation.
    • Yes: it works in both equations.

  7. Luz gets (4, -3) for the system y = -x + 1 and 2x - 3y = 17. Is (4, -3) a solution of the system?

    • Yes: it works in both equations.
    • No: it works in neither equation.
    • No: it works only in the second equation.
    • No: it works only in the first equation.

  8. Ari looks at the system y = 3x - 2 and 6x - 2y = 4 and tries substitution. How many solutions does the system have?

    • no solution
    • infinitely many solutions
    • exactly one solution

  9. Tala gets y = -2x + 3 and 4x + 2y = 6 as a bonus question (the bonus is bragging rights). How many solutions does the system have?

    • exactly one solution
    • no solution
    • infinitely many solutions

  10. Bo looks at the system y = 2x + 3 and x + y = 3 and tries substitution. How many solutions does the system have?

    • infinitely many solutions
    • exactly one solution
    • no solution
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8th grade Solve a system by substitution worksheet – printable
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About this worksheet

Solve a system by substitution. Every version has 10 questions, and the answer key prints on the second page.

What your child will learn

  • I can put the rule for y into the other equation, solve for x, and then find y: the solution is the point (x, y).
  • I can multiply out a bracket such as 3(x − 3) correctly while I substitute.
  • I can tell from the last line whether a system has one solution, no solution (a false line such as 3 = 9) or infinitely many (a true line such as 4 = 4).

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 row both tables share.

substitution: Putting what one letter equals into the other equation, in its place.

bracket: The ( ) that keeps a rule together, so the number outside multiplies all of it.

last line: The line the work ends with, such as x = 4, 3 = 9 or 4 = 4.

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 found one of the two numbers of the answer and stopped.

What to say

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

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

Ask: what is the other letter at that spot?

Questions parents ask

What is the most common mistake with solve a system by substitution?

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 substitution?

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

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