Solving Systems by Elimination
I can solve a system by adding or subtracting the equations to eliminate a variable.
The problem this sheet solves
Elimination fails on the add-or-subtract decision. Opposite coefficients cancel by adding; equal ones cancel by subtracting; and a student who adds equal terms gets 4y, loses nothing, yet carries on to a clean-looking answer. Knowing when to multiply an equation first, and that it must reach BOTH sides, is the second half. This sheet makes the decision explicit before any arithmetic happens: look at the coefficients, then choose. Equations are set in columns so like terms line up visually, and multiplying a whole equation is treated as scaling both sides, which is where the other common slip lives.
The key rule
Line the equations up in columns. If the coefficients of one variable are OPPOSITE, add. If they are EQUAL, subtract. If they are neither, multiply a whole equation — both sides — until they are.
Opposites add. Equals subtract. Adding equal terms doubles them.
Watch out
The mistake: The y-terms are both + 2y, and a student ADDS the equations, writes 4x = 24, and gets x = 6.
The fix: Equal coefficients cancel by SUBTRACTING: 2x = 8, so x = 4 and y = 2. Adding 2y to 2y gives 4y — the y does not leave, and 6 is a whole number, so the mistake does not look like one.
What is included
- Reference page — student-friendly definitions, a worked example, a Watch Out error pair, and the key rule
- Practice page — six problems, building from foundational to multi-step
- Apply page — a word problem, a reasoning prompt, and an error-analysis task
- Assess — a half-page exit ticket, two to a sheet, with a score box
- Full answer key — every item worked, plus a grading guide that says what each wrong answer tells you
- Ink-saver edition of all 7 pages
- 14-slide teacher deck (PowerPoint) with presenter notes on every slide
Standard codes refer to the Common Core State Standards for Mathematics. Math Class 678 is an independent publisher, not affiliated with, sponsored by, or endorsed by NGA Center or CCSSO. Every product is sold on Teachers Pay Teachers.