Elimination Method — SAT Math Explained
A method for solving systems of equations where you add or subtract the equations (sometimes after multiplying) to eliminate one variable, leaving a single-variable equation to solve.
The Core Idea
If two equations have opposite coefficients for a variable, adding them makes that variable disappear. You engineer this 'cancellation' deliberately by multiplying equations by constants before adding.
Step-by-Step: How to Approach Elimination Method
Arrange both equations in standard form: Ax + By = C
Look for a variable with opposite coefficients (e.g., +3x and -3x) — if found, add directly
If not, multiply one or both equations by constants so one variable's coefficients become opposites
Add the two equations together — one variable cancels out
Solve for the remaining variable
Substitute back into either original equation to find the other variable
Check in both equations
When To Use Elimination
Both equations are in standard form (Ax + By = C)
Coefficients are already equal or easily made equal by multiplying by small numbers
Substitution would create messy fractions
Multiplication Strategy
If x-coefficients are 2 and 3, multiply the first equation by 3 and the second by 2 (or use negatives to create opposites)
Find the LCM of the coefficients to determine what to multiply by
Common Errors to Avoid
Adding when you should subtract (if coefficients are the same sign, you subtract to cancel)
Only multiplying part of an equation instead of every term
Not checking the solution in both original equations
Practice: Elimination Method
5 SAT-style questions. Select your answer and get an instant explanation.
Solve using elimination: x + y = 8 and x - y = 2
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