Substitution Method — SAT Math Explained
A method for solving systems of equations where you solve one equation for one variable, then substitute that expression into the other equation to solve for the remaining variable.
The Core Idea
Substitution reduces a two-variable system into a one-variable equation you already know how to solve. It works especially well when one equation is already solved for a variable or easily can be.
Step-by-Step: How to Approach Substitution Method
Choose one equation and solve it for one variable (pick the easiest — look for a coefficient of 1)
Substitute that expression into the OTHER equation, replacing the variable everywhere it appears
Solve the resulting single-variable equation
Plug the found value back into either original equation to find the second variable
Write the solution as an ordered pair (x, y)
Check by substituting both values into BOTH original equations
When To Use Substitution
One equation is already solved for a variable (e.g., y = 3x - 1)
A variable has a coefficient of 1 or -1, making isolation easy
The coefficients don't align well for elimination
Strategy Tips
Label which equation is #1 and #2 to stay organized
If fractions appear during substitution, consider switching to elimination instead
Common Errors to Avoid
Substituting back into the same equation you solved — always use the OTHER equation
Not distributing properly when substituting an expression
Forgetting to find the second variable after finding the first
Not checking the answer in both equations
Practice: Substitution Method
5 SAT-style questions. Select your answer and get an instant explanation.
Solve using substitution: y = 2x and x + y = 9
Want More Substitution Method Practice?
Blitzsat's question bank has thousands of SAT-style questions across every topic in Algebra. Filter by topic and difficulty. Get AI-powered questions generated from your own notes.
Practice & Explore: Substitution Method
Apply what you just learned — practice questions, full tests, and related study resources.