Grade 8 · Math

8th grade Solve a system by substitution worksheet

6 printable versionsBuilding Confidence10 questions · answer keyFree · no account

Level: Building Confidence · On Level · Challenge Me

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Solve a system by substitution

Grade 8 Math Worksheet - Building Confidence

NameDate

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

Kira's riddle card has two clues: y = 2x and x + y = 12. Replacing y with 2x gives x + (2x) = 12. What is the solution (x, y)?
Noah solves y = 3x and x + y = 20, pencil tapping. Putting 3x in for y gives x + (3x) = 20. What is the solution (x, y)?
A puzzle on the board says y = 4x and 2x + y = 18. Ren replaces y with 4x and gets 2x + (4x) = 18. What is the solution (x, y)?
Read this first
Use this
Two rules (x = weeks, y = height in cm). Bean plant: y = 2x + 3. Sunflower: y = x + 7.
Pia's bean plant is racing the sunflower. Pia sets the two height rules equal: 2x + 3 = x + 7. At which point (weeks, cm) are the two plants the same height?
Use this
Two rules (x = days, y = snow depth in cm). Sunny yard: y = -5x + 40. Shady yard: y = -2x + 25.
Snow melts in two yards. Jun sets the two depth rules equal: -5x + 40 = -2x + 25. At which point (days, cm) is the snow the same depth in both yards?
6.
A homework card shows y = x + 4 and 3x + 5y = 44. Which equation comes next when Zee replaces y with x + 4?
- 3x + 5y = x + 4
- 3(x + 4) + 5y = 44
- 3x + 5(x + 4) = 44
- 3x + 5x + 4 = 44
7.
Bo guesses that (3, 5) solves y = 3x and x + 2y = 13, a lucky guess maybe. Is (3, 5) a solution of the system?
- No: it works only in the second equation.
- No: it works in neither equation.
- Yes: it works in both equations.
- No: it works only in the first equation.
8.
Kira gets (3, 7) for the system y = 2x + 1 and 3x + y = 16. Is (3, 7) a solution of the system?
- No: it works only in the second equation.
- Yes: it works in both equations.
- No: it works in neither equation.
- No: it works only in the first equation.
9.
Zee solves y = 2x + 5 and y = -x + 5 by substitution. The work ends with the line 3x = 0. How many solutions does the system have?
- no solution
- infinitely many solutions
- exactly one solution
10.
Ren checks a system on scrap paper: y = 4x - 1 and y = 2x - 1. Substitution ends with 2x = 0. How many solutions does the system have?
- exactly one solution
- no solution
- infinitely many solutions

8th grade Solve a system by substitution worksheet – printable — Print: 1 2 3 4 5 6

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

See all grade 8 math

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