Solve the pair of equations $2 x + 3 y = 7$ and $x - y = 1$ by the method of substitution.

easy MCQ 1 mark Class 10 · Mathematics · Pair of Linear Equations in Two Variables

Answer

x = 2, y = 1

The correct answer is $x = 2, y = 1$ — Substitute $y = 1$ back into $x = y + 1$ to get $x = 2$ .

Step-by-step solution

From the second equation, express $x$ as $x = y + 1$ because substitution requires one variable in terms of the other.
Substitute $x = y + 1$ into the first equation: $2 (y + 1) + 3 y = 7$ .
Simplify: $2 y + 2 + 3 y = 7 \Rightarrow 5 y + 2 = 7$ .
Subtract 2 from both sides: $5 y = 5$ .
Divide by 5: $y = 1$ .
Substitute $y = 1$ back into $x = y + 1$ to get $x = 2$ .

Common mistake: Forgetting to substitute

x = y + 1

correctly, leading to

2 y + 3 y = 7

instead of

2 (y + 1) + 3 y = 7

Concept tested: Substitution method