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MathidiaMathematics Academy
Simultaneous equations
Lesson 30 of 75
Review

Check simultaneous solutions

Objective. Substitute a pair into both original equations.

  1. 1. Learn
  2. 2. Worked example
  3. 3. Practice
  4. 4. Feedback
  5. 5. Continue

Learn: the key idea

Checking a simultaneous solution means substituting the found pair of values back into both original equations to confirm they make each one true. This step catches arithmetic slips made during elimination or substitution, since an error usually causes one equation to fail even if the other happens to balance. For example, if x = 2 and y = 3 are proposed solutions to x + y = 5 and 2x − y = 1, substituting gives 2 + 3 = 5 (true) and 2(2) − 3 = 1 (true), confirming the solution is correct. If either equation does not balance, the working must be revisited to find the mistake.

Worked example

Verify whether x = 4 and y = 1 is a correct solution to the simultaneous equations 3x − y = 11 and x + 2y = 6.

4 … 1
Coordinate grid with the line 4 … 1
  1. 1Substitute into the first equation: 3(4) − 1 = 12 − 1 = 11, which matches the right-hand side.
  2. 2Substitute into the second equation: 4 + 2(1) = 4 + 2 = 6, which matches the right-hand side.
  3. 3Both equations balance with these values.
  4. 4Since both checks are true, the solution is confirmed correct.

Answer: Yes, x = 4 and y = 1 satisfy both equations

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Practice

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Common mistake. Pupils often check their solution in only one of the two original equations and assume it is correct, missing an error that only shows up in the other equation. Always substitute into both original equations before concluding the solution is right.

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