x = y + 2 and 2x + y = 10
Show answer
(4, 2)
Free printable worksheet
Systems by Substitution Worksheet
Fourteen advanced systems requiring isolation, division, rearrangement, and substitution.
Algebra 1Grades 7-104 pagesAnswer key included
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What this worksheet includes
- Fourteen advanced systems requiring isolation, division, rearrangement, and substitution.
- 4-page printable PDF with a complete answer key
- Designed for Grades 7-10 algebra 1 practice
- Available as an immediate free download with no email required
How to use it
Use this systems by substitution worksheet for guided practice, independent review, homework, tutoring sessions, or a quick skills check. The spacious layout is designed to leave room for students to show their work rather than guess from crowded answer choices.
After students finish, compare their reasoning with the included answer key. When an answer is incorrect, have the student locate the first step where their work changed direction before trying the problem again.
Who this practice is for
This resource is designed for grades 7-10 students working on algebra 1. Teachers, tutors, homeschool families, and parents can preview the first page before deciding whether the level and spacing fit the student.
Looking for a broader sequence? Browse all Algebra I worksheets.
Topic guide
How to approach systems by substitution
Substitution replaces a variable with an equivalent expression from the other equation. When neither variable is isolated, begin by rearranging one equation and choose the variable that produces the simplest expression.
The advanced problems require division, distribution, and collecting terms after substitution. Parentheses around the substituted expression are essential whenever a coefficient applies to the entire expression.
Learning objectives
- Select and isolate an efficient variable
- Substitute an entire expression using parentheses
- Solve for the second coordinate and check both equations
Skills to review first
- Solving linear equations
- Rearranging formulas
- Distribution with signed numbers
Worked example
Follow the reasoning step by step
Solve y = 2x − 1 and 3x + y = 14.
- Replace y in the second equation with 2x − 1.
- Solve 3x + (2x − 1) = 14, giving 5x = 15.
- Find x = 3, then substitute into y = 2x − 1.
- Find y = 5 and check the pair in both equations.
Solution: (3, 5).
Try before downloading
Three sample problems
Work each problem, then open the answer to check your result.
x + y = 7 and 2x − 3y = 4
Show answer
Isolate x = 7 − y; solution (5, 2).
2x + y = 1 and 3x − 2y = 12
Show answer
Use y = 1 − 2x; solution (2, −3).
Error check
Common mistakes to watch for
- Substituting into the same equation used to isolate the variable
- Dropping parentheses around a multi-term expression
- Finding x but forgetting to return for y