Determine whether the pair of equations $5 x - 2 y = 7$ and $10 x - 4 y = 20$ are consistent, inconsistent, or represent the same straight line. Justify your answer.

medium 3 marks Class 10 · Mathematics · Pair of Linear Equations in Two Variables

Answer

Inconsistent (parallel lines, no common solution).

The correct answer is Inconsistent (parallel lines, no common solution). — Hence, the equations are inconsistent.

Step-by-step solution

Write the two equations: (1) $5 x - 2 y = 7$ and (2) $10 x - 4 y = 20$ .
Observe that equation (2) is exactly twice equation (1) on the left side: $2 \times (5 x - 2 y) = 10 x - 4 y$ .
Multiply the right side of (1) by 2: $2 \times 7 = 14$ .
Since the left sides are proportional but the right sides are not (14 $\neq =$ 20), the two equations represent parallel lines.
Parallel lines have no point of intersection, therefore the system is inconsistent.
Hence, the equations are inconsistent.

Common mistake: Assuming that because the left sides are proportional, the equations must be the same line, ignoring the constants.

Concept tested: Consistency of linear equations

Published 19 August 2026 · Last updated 16 September 2026 · How this solution was prepared and checked