Solving Systems of Equations: Substitution vs Elimination
Two core methods for simultaneous equations, when to use each, and what no solution or infinitely many solutions look like.
By AI Math Solver Team · · 6 min read
A system of equations asks for values that satisfy every equation at once.
Substitution
Solve one equation for a variable, substitute into the other.
Best when a variable already has coefficient 1.
Elimination
Add or subtract equations to cancel a variable.
Multiply the second equation by 3 and add: , so , .
Special cases
- No solution: you reach a false statement like (parallel lines).
- Infinitely many: you reach (the same line twice).
Check your work with the System of Equations Calculator.
#systems of equations#elimination#substitution