Grade 8 · Math

8th grade Solve a system by substitution worksheet

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Solve a system by substitution

Grade 8 Math Worksheet - Challenge Me

NameDate

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

Pia solves 2x + y = 5 and 5x + 2y = 9 by substitution. Neither equation starts with y alone. What is the solution (x, y)?
Ren's puzzle card shows -2x + y = 3 and 5x - 2y = -4, with a doodle of a very calm cat. What is the solution (x, y)?
Noah's system is x = 2y + 1 and -2x + 5y = 0. The first rule tells what x is. What is the solution (x, y)?
Milo solves x = 3y + 1 and -2x + 3y = -5 by putting the rule for x into the other equation. What is the solution (x, y)?
Luz meets a system with x alone: x = -2y + 4 and 4x + 5y = 7. What is the solution (x, y)?
Tala measures a pepper plant (x cm) and a tomato plant (y cm): y = 2x + 3 and x + y = 36. What point (pepper cm, tomato cm) solves the system?
Ari unwinds two kite strings, blue (x m) and red (y m): y = 2x + 4 and x + y = 64. What point (blue m, red m) solves the system?
8.
Zee solves 3x + y = 4 and 6x + 2y = 8 by getting y alone first. How many solutions does the system have?
- no solution
- exactly one solution
- infinitely many solutions
9.
Pia finds -2x + y = -1 and 8x - 4y = 4 on the back of a worksheet (a mystery bonus). How many solutions does the system have?
- infinitely many solutions
- no solution
- exactly one solution
10.
Noah finds -4x + y = -2 and x + 2y = -4 on the back of a worksheet (a mystery bonus). How many solutions does the system have?
- infinitely many solutions
- no solution
- exactly one solution

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

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)

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.

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.

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?

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.

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