➕ Algebra 1 · Systems of Equations
Solving Systems by Elimination cheat sheet
Everything you need on one page. Print it, or switch on test-yourself mode to blur the answers and check your memory.
The plan (LAMBS)
- L: Line up in standard form
- A: Adjust (multiply every term) so a variable matches
- M: Merge (add or subtract) and solve
- B: Back-substitute for the other variable
- S: Show it works in both original equations
Which move?
- Opposite coefficients (like 2y and −2y): add
- Equal coefficients (like 3x and 3x): subtract, and the minus reaches every term
- Neither (like 2x and 5x): multiply one or both equations, every term, then add or subtract
Special cases
- Both variables vanish, false (0 = 17): no solution (parallel lines)
- Both variables vanish, true (0 = 0): infinitely many solutions (same line)
- 0 = 0 does not mean x = 0 and y = 0
Example
- 3x + 2y = 12 and 5x − 2y = 4
- Add: 8x = 16, so x = 2
- Back-substitute: 6 + 2y = 12, so y = 3
- Solution: (2, 3)
Watch out
- Subtract every term of the second equation
- Multiply the constant too
- The answer is a pair, so check both equations
Formulas
- Standard form: Ax + By = C
- Adding equations: If A = B and C = D, then A + C = B + D
- Subtracting equations: If A = B and C = D, then A − C = B − D
- Multiplying an equation: A = B and kA = kB have the same solutions when k ≠ 0
Solving Systems by Elimination cheat sheet from HighSchoolQ.com, for personal study use.