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

Step-by-step solution

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

Concept tested: Consistency of linear equations

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