Check a solution by substitution.
Substitute the proposed value into the original equation and check whether both sides are equal.
Core Idea
To verify a solution, substitute the value back into the original equation and confirm that both sides are equal.
Understanding
Substitution is your error-catcher. After solving, plug the answer back into the original equation (not a simplified version) and see if the left side equals the right side.
This works in reverse too. If a problem gives you a value and asks whether it's a solution, substitute it and check. No solving required — just arithmetic.
On the SAT, substitution is also a powerful strategy for multiple choice. If you're stuck on an equation, try each answer choice. The one that makes both sides equal is correct. Start with choices that are easy to compute — whole numbers, zero, or small values.
Step by Step
- Take the proposed solution value.
- Replace every instance of the variable in the original equation with that value.
- Simplify both sides of the equation independently.
- If both sides are equal, the value is a valid solution. If not, it is not.
Misconceptions
- Substituting into a partially simplified equation instead of the original — earlier simplification errors won't be caught this way.
- Making arithmetic mistakes during substitution (especially with negatives) and concluding the wrong answer is correct.
- Assuming a solution is wrong because the check gives a non-obvious equality — always simplify both sides fully before comparing.
Worked Example
Which value of
Select an answer to see the explanation