Pair of Linear Equations

What you'll learn

Learn how a pair of linear equations in two variables works, the three types of solutions, and how to solve them by elimination with a step-by-step worked example.

This chapter has

Pair of Linear Equations — solved practice questions

6 Class 10 Mathematics questions with step-by-step solutions. Attempt each, then reveal the answer.

1. Q1easy

   The graph of a linear equation in two variables is a:

   • Acircle
   • Bparabola
   • Cstraight line
   • Dcurve
   Show answer & solution

   Correct answer: (C) straight line

   Any equation of the form ax + by + c = 0 graphs as a straight line.

2. Q2easy

   A pair of two intersecting lines has how many solutions?

   • Ano solution
   • Bexactly one
   • Ctwo
   • Dinfinitely many
   Show answer & solution

   Correct answer: (B) exactly one

   Intersecting lines meet at exactly one point, giving a unique solution.

3. Q3medium

   The pair x + y = 5 and 2x + 2y = 10 has:

   • Ano solution
   • Bexactly one solution
   • Cinfinitely many solutions
   • Dtwo solutions
   Show answer & solution

   Correct answer: (C) infinitely many solutions

   The second equation is just twice the first — they are the same line, so there are infinitely many solutions.

4. Q4medium

   Solve x + y = 7 and x − y = 3. What is the value of x?

   • A3
   • B4
   • C5
   • D6
   Show answer & solution

   Correct answer: (C) 5

   Add the equations: 2x = 10 → x = 5 (and y = 2).

5. Q5medium

   The pair x + y = 4 and x + y = 6 has:

   • Ano solution
   • Bone solution
   • Cinfinitely many
   • Dtwo solutions
   Show answer & solution

   Correct answer: (A) no solution

   Same left side but different right side → parallel lines that never meet → no solution.

6. Q6hard

   If a pair of linear equations is consistent, the lines are:

   • Aalways parallel
   • Bintersecting or coincident
   • Calways perpendicular
   • Dnever meeting
   Show answer & solution

   Correct answer: (B) intersecting or coincident

   Consistent means at least one solution exists — the lines either intersect (one solution) or are coincident (infinitely many).

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