ncertmate
Open navigation menu
Class 10
Subjects
Mathematics Science Social Science Civics Social Science Economics Social Science Geography Social Science History
Search
NCERT solutions

Pair of Linear Equations in Two Variables

All 6 textbook questions with direct answer previews. Open any question for simple explanations and exam-ready answers.

Back to chapter hub Important Questions

All questions

6
Q1

What is a pair of linear equations in two variables? Write its general form and explain what a solution means.

A pair of linear equations in two variables has the form a1x+b1y+c1=0a_1x+b_1y+c_1=0 and a2x+b2y+c2=0a_2x+b_2y+c_2=0. A solution is an ordered pair (x,y)(x,y) satisfying both equations.
Show Answer
Q2

Explain the three graphical possibilities for a pair of linear equations.

The two lines may intersect at one point, be parallel, or coincide. Intersecting lines give one solution; parallel lines give no solution; coincident lines give infinitely many solutions.
Show Answer
Q3

State the ratio test for consistency of a1x+b1y+c1=0a_1x+b_1y+c_1=0 and a2x+b2y+c2=0a_2x+b_2y+c_2=0.

If a1a2≠b1b2\frac{a_1}{a_2}\ne\frac{b_1}{b_2}, there is one solution. If a1a2=b1b2≠c1c2\frac{a_1}{a_2}=\frac{b_1}{b_2}\ne\frac{c_1}{c_2}, there is no solution. If all three ratios are equal, there are infinitely many solutions.
Show Answer
Q4

Solve x−2y=0x-2y=0 and 3x+4y=203x+4y=20 by substitution.

From x−2y=0x-2y=0, x=2yx=2y. Substitute in 3x+4y=203x+4y=20: 3(2y)+4y=203(2y)+4y=20, so 10y=2010y=20, y=2y=2. Hence x=4x=4.
Show Answer
Q5

Solve 2x+3y=112x+3y=11 and 2x−y=32x-y=3 by elimination.

Subtract the second equation from the first: (2x+3y)−(2x−y)=11−3(2x+3y)-(2x-y)=11-3, so 4y=84y=8, y=2y=2. Substitute in 2x−y=32x-y=3: 2x−2=32x-2=3, so x=52x=\frac52.
Show Answer
Q6

State the cross-multiplication formula for solving a pair of linear equations.

For a1x+b1y+c1=0a_1x+b_1y+c_1=0 and a2x+b2y+c2=0a_2x+b_2y+c_2=0, xb1c2−b2c1=yc1a2−c2a1=1a1b2−a2b1\frac{x}{b_1c_2-b_2c_1}=\frac{y}{c_1a_2-c_2a_1}=\frac{1}{a_1b_2-a_2b_1}, provided a1b2−a2b1≠0a_1b_2-a_2b_1\ne0.
Show Answer

Other Chapters