SAT Math: Solving Systems of Equations by Substitution
35+ practice questions in Praczo
The concept, explained
- 1
Substitution works by solving one equation for one variable, then plugging that expression into the other equation to create one equation with one unknown.
- 2
Choose the variable that's easiest to isolate — usually whichever already has a coefficient of 1 or −1.
- 3
After substituting, solve the resulting single-variable equation, then back-substitute to find the second variable.
- 4
Always check your solution by plugging both values back into both original equations — both must be satisfied.
- 5
If you end up with a contradiction (e.g., 0 = 5), the system has no solution. If you get a true statement (e.g., 0 = 0), it has infinitely many solutions.
- ✗ Substituting into the same equation you solved from — always substitute into the other equation.
- ✗ Finding x and stopping. Re-read the question — it may ask for y, or x + y, or some other expression.
SAT-style practice
y = 3x − 1 2x + y = 9 What is the value of x?
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