Calculator Skills
Checking Equation Answers with a Calculator
The fastest way to catch a wrong solution is to substitute it back, and the calculator makes that a few keystrokes.
Substitute the answer back
After solving an equation, type the original expression with your answer in place of the variable. If both sides match, the answer is right.
This catches sign errors and slips in seconds, and works for quadratics, simultaneous equations and more.
A worked keystroke sequence for substitution
- Suppose you solved x² − 7x + 12 = 0 and got x = 4. To check it, substitute 4 back in.
- Enter 4 x² − 7 × 4 + 12 and press = . The display reads 0, so x = 4 satisfies the equation.
- Test the other root the same way: enter 3 x² − 7 × 3 + 12 = . You get 9 − 21 + 12 = 0, so x = 3 works too.
- Both roots return zero, confirming the factorisation (x − 3)(x − 4) = 0 without re-solving from scratch.
Watch the sign when you substitute
The most common mistake in a substitution check is dropping a sign on a negative root. If a root is x = −5 and the term is −7x, then −7 × (−5) = +35, not −35.
Put brackets around any negative value you substitute so the calculator handles the sign correctly. If your check does not come out to zero, re-do the substitution slowly before assuming the solution itself is wrong, often the error is only in the check.
Source:SPM: Format Pentaksiran mulai 2021, Matematik (1449)
Frequently asked questions
How do I check a solution to an equation with the calculator?
Substitute your value back into the original equation and evaluate. If both sides come out equal, for an expression set to zero, if the result is zero, the solution is correct.
This substitution check takes only a few keystrokes and catches most sign and arithmetic slips before you move on.
My substitution does not give zero, is my answer definitely wrong?
Not necessarily, the error might be in the check. First re-enter the substitution carefully, using brackets around any negative value so the signs are handled correctly.
Only if the corrected check still does not give zero should you go back and re-solve the equation. Careless substitution is a common false alarm.
Can I check simultaneous equations the same way?
Yes. Substitute your pair of values into both original equations and confirm each one balances.
Both must hold, not just one, because a correct solution satisfies every equation in the set at the same time. Checking both equations catches a value that happens to fit one line but not the other.