Substitution method
- CBSE · NCERT Class 10, Ch 3 Pair of Linear Equations in Two Variables
The substitution method solves a pair of linear equations by writing one variable in terms of the other, then putting that into the second equation.
It turns two equations in two unknowns into one equation in one unknown. That one is easy to solve. You then put the value back to find the other unknown.
- Step 1: from one equation, write y in terms of x, or x in terms of y.
- Step 2: put this into the other equation and solve it.
- Step 3: put that value back into Step 1 to find the other unknown.
- Step 4: check both values in both original equations.
A small example
Solve x + y = 11 and 2x = y + 1. From the first, y = 11 - x. Put this into the second: 2x = 12 - x, so 3x = 12 and x = 4. Then y = 11 - 4 = 7. Check: 4 + 7 = 11, and 2 × 4 = 8 = 7 + 1.
If a step gives a false statement such as 0 = 5, the pair has no solution. If it gives a true one such as 0 = 0, the pair has endless solutions.
Where marks go
Question 4 of CBSE's 2026-27 Maths Basic sample paper is this pair, set as a fraction puzzle. The top and bottom of a fraction add to 11. Adding 1 to the bottom makes the fraction 1/2. The answer is 4/7. It is a 1-mark multiple-choice question with no part marks.
In longer questions, the board's Maths Basic marking scheme for 2026-27 does not name a method. In Question 31 it says only "Solving (1) and (2), we get", and gives 1 mark for the solution under step marking. So any correct method can lead to that mark, including the elimination method.
Sources
Facts last checked against these sources on 30 September 2026.
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