How to Solve Pair of Linear Equations — Step by Step Guide

Solve two equations simultaneously using substitution, elimination and graphical methods. This guide covers Class 9 to 10.

Step-by-Step Method

  1. 1

    Write both equations in the form ax + by = c.

  2. 2

    Substitution method: solve one equation for a variable and substitute into the other.

  3. 3

    Elimination method: make the coefficients of one variable equal, then add or subtract the equations.

  4. 4

    Graphical method: plot both lines and find their point of intersection.

  5. 5

    Check: a₁/a₂ ≠ b₁/b₂ → unique solution. a₁/a₂ = b₁/b₂ ≠ c₁/c₂ → no solution. a₁/a₂ = b₁/b₂ = c₁/c₂ → infinite solutions.

Worked Example

Problem: Solve: x + y = 10 and x - y = 4.

Solution: Add both equations: 2x = 14, so x = 7. Substitute: 7 + y = 10, so y = 3. Solution: (7, 3).

Common Mistakes to Avoid

  • ✗

    Making arithmetic errors during elimination — double-check all steps.

  • ✗

    Solving for only one variable and forgetting to find the other.

  • ✗

    Not verifying the solution by substituting into BOTH original equations.

  • ✗

    Incorrectly multiplying all terms when trying to make coefficients equal.

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CBSE Class 10 Pair of Linear Equations

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Frequently Asked Questions

How do I solve Pair of Linear Equations problems?
Write both equations in the form ax + by = c. Substitution method: solve one equation for a variable and substitute into the other.
What are common mistakes in Pair of Linear Equations?
Making arithmetic errors during elimination — double-check all steps. Solving for only one variable and forgetting to find the other.
Which class covers Pair of Linear Equations?
Pair of Linear Equations is typically taught in Class 9, 10. SparkEd has free practice for all these grades.
Where can I practise Pair of Linear Equations for free?
SparkEd offers free chapter-wise practice for Pair of Linear Equations aligned to CBSE, ICSE, and IB curricula. Visit sparkedmaths.com to start.

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