C
CraftExam
medium difficulty6 min

Checking obtained solution in both equations

Checking means substituting the obtained values of x and y into both equations to confirm that the pair is correct.

In one line: Solved is not finished until checked.

Practice This Concept

Understand it

A solution is only accepted after verification in both equations. This step prevents careless arithmetic errors and sign mistakes from going unnoticed. In board exams, checking is especially useful after elimination or substitution because one small mistake can spoil the entire answer.

Example

If x = 2 and y = 3 are obtained, substitute them into both equations and confirm that each equation becomes true.

Formula and rule

Substitute the obtained x and y in each original equation and verify that both left and right sides match.

See it worked out

Follow the example line by line, then use the same method on new questions.

Worked example

  1. 1If a student gets x = 3 and y = 1 for 2x + y = 7 and x - y = 2, then 2(3) + 1 = 7 and 3 - 1 = 2.
  2. 2Since both are true, the answer is correct.

Method you can reuse

  1. 1Take the final x and y values.
  2. 2Substitute them into the first equation.
  3. 3Substitute them into the second equation.
  4. 4Confirm both results.
  5. 5If any equation fails, go back and find the error.

Visual tip

A small two-row check table can help: equation one, equation two, and substituted result.

Check yourself

Answer the question in your head before opening the answer.

Try it yourself

Why should a solved pair be checked in both equations before finalising the answer?

Think first, then show answer
Because both equations must be satisfied together. Checking in both equations confirms that the ordered pair is correct and helps catch sign or calculation mistakes.

Common wrong answer

A common wrong answer is to accept the first neat answer obtained during working without verification. That can hide a sign slip.

Don't mix this up

Students often check the answer in only one equation and assume the pair is correct.

Exam tip

A quick verification can save marks when a sign error slipped into the solution process.

Write it in the exam

Each point is worth about one mark. Write point 1 for a 1-mark question and keep adding points as the marks go up.

How CBSE asks it

The exam may ask students to verify the solution or identify an incorrect step by checking the final pair.
  1. 1

    Enough for 1 mark

    Checking means substituting the obtained values of x and y into both equations to confirm that the pair is correct.

  2. 2

    Add for 2 marks

    Example: If x = 2 and y = 3 are obtained, substitute them into both equations and confirm that each equation becomes true.

  3. 3

    Add for 3 marks

    A solution is only accepted after verification in both equations.

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