➕ Algebra 1 · Systems of Equations
Solving Systems by Substitution 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 steps (SWAP, then check)
- S: Solve one equation for a variable
- W: Write it in the other equation, in parentheses
- A: Algebra: solve for the one variable left
- P: Plug back in to find the other variable
- Then check both original equations
Special cases (variables vanish)
- True leftover (like 12 = 12): infinitely many solutions
- False leftover (like 4 = 7): no solution
- A variable is left: one solution
Parentheses and signs
- Wrap the expression: 3x − 2(x − 5)
- Minus flips every sign: x − (2y − 5) = x − 2y + 5
- Negative values: 3(−2) + 5
Example
- y = 3x − 4 and 2x + y = 11
- 2x + (3x − 4) = 11, so 5x = 15 and x = 3
- y = 3(3) − 4 = 5
- Solution (3, 5)
Watch out
- Parentheses first
- Use the other equation
- Check in both originals
Formulas
- The swap: If y = E (where E is an expression), replace y with (E) in the other equation
- Minus before parentheses: a − (b + c) = a − b − c and a − (b − c) = a − b + c
- True leftover: Variables vanish and the statement is true (like 12 = 12): infinitely many solutions
- False leftover: Variables vanish and the statement is false (like 4 = 7): no solution
Solving Systems by Substitution cheat sheet from HighSchoolQ.com, for personal study use.