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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.

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Student-friendly explanation

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.

How to write this in exams

  1. 1

    Start with the exact idea

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

  2. 2

    Then show how to use it

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

  3. 3

    Add one concrete example

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

  4. 4

    Avoid this incomplete answer

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

Definition

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

Example

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

Rule to remember

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

Memory hook

Solved is not finished until checked.

Examples and method

Worked example

If 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. Since both are true, the answer is correct.

Method to apply

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

Diagram support

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

How CBSE asks it

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

Avoid common mistakes

Common confusion

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

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.

Exam tip

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

Quick check

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

Answer writing and exam use

1-mark answer

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

2-mark answer

Checking means substituting the obtained values of x and y into both equations to confirm that the pair is correct. Substitute the obtained x and y in each original equation and verify that both left and right sides match. If x = 2 and y = 3 are obtained, substitute them into both equations and confirm that each equation becomes true.

3-mark answer

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. Substitute the obtained x and y in each original equation and verify that both left and right sides match. If 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. Since both are true, the answer is correct. The exam may ask students to verify the solution or identify an incorrect step by checking the final pair. A common wrong answer is to accept the first neat answer obtained during working without verification. That can hide a sign slip.
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