Elimination method
- CBSE · NCERT Class 10, Ch 3 Pair of Linear Equations in Two Variables
The elimination method solves a pair of linear equations by adding or subtracting them so that one variable cancels out.
First, multiply one or both equations so that one variable has the same coefficient in both. Then subtract or add the equations. That variable drops out, leaving one equation in one unknown. Solve it, then put the value back to find the other unknown.
A small example
A company sold 1000 bottles of sanitiser in June. Small ones cost ₹10 and large ones ₹15. Total sales were ₹12,750. Let x be the number of small bottles and y the number of large ones.
- x + y = 1000
- 10x + 15y = 12750
- Multiply the first by 10: 10x + 10y = 10000.
- Subtract it from the second: 5y = 2750, so y = 550.
- Then x = 1000 - 550 = 450.
Where marks go
This is Question 36 of CBSE's 2026-27 Maths Standard sample paper, one of its case-based questions. Part (iii)(A) is worth 2 marks. The board's Maths Standard marking scheme for 2026-27 gives 1 mark for writing the two equations. It gives 1 mark for solving them to get 450 and 550.
Parts (i) and (ii) of the same question give 1 mark each just for forming an equation. So in this question, forming equations carries 3 of the 4 marks. Solving carries 1. The scheme writes "Solving (i) and (ii), we get" and names no method, so substitution earns that mark too.
Sources
Facts last checked against these sources on 30 September 2026.
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