Pair of linear equations in two variables
- CBSE · NCERT Class 10, Ch 3 Pair of Linear Equations in Two Variables
A pair of linear equations in two variables is two equations, each of the form ax + by + c = 0, in the same two unknowns x and y.
Each equation, drawn on a graph, is a straight line. Solving the pair means finding the values of x and y that make both equations true at once. On the graph, that is the point where the two lines meet.
The chapter solves pairs in two ways. The graphical method draws both lines. The algebraic methods are the substitution method and the elimination method.
A small example
The digits of a two-digit number add up to 9. Nine times the number equals twice the number with its digits reversed. Let the tens digit be x and the units digit be y. The number is 10x + y.
- First equation: x + y = 9.
- Second equation: 9(10x + y) = 2(10y + x). This simplifies to 88x = 11y, or y = 8x.
- Put y = 8x into the first: 9x = 9, so x = 1 and y = 8. The number is 18.
Where marks go
This is Question 31 of CBSE's 2026-27 Maths Basic sample paper, worth 3 marks. The board's Maths Basic marking scheme for 2026-27 gives half a mark for writing the number as 10x + y. It gives half a mark for each of the two equations, 1 mark for solving them, and half a mark for the answer, 18.
So 1.5 of the 3 marks are for turning the words into algebra, before any solving. Each of those lines is a separate step under step marking.
Sources
Facts last checked against these sources on 30 September 2026.
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