How will the graphs of (5x-10y=20) and (x-2y=4) be?

Correct answer: Coincident

The direct answer is C: the graphs are coincident. The first equation is \(5x-10y=20\). Divide every term by 5, which is nonzero: \(x-2y=4\). This is exactly the second equation, so both equations describe the same straight line. Every point on that line satisfies both equations, giving infinitely many common solutions. Option A, intersecting at one point, would describe two different non-parallel lines, but these equations are identical after simplification. Option B, parallel and distinct, would require different lines with the same direction, not the same equation. Option C is correct because the two graphs lie exactly on top of each other. Option D, like axes, is not a standard conclusion and is not supported by these equations; the lines are not generally the coordinate axes. Exam cue: simplify both equations first. If one becomes exactly the other, the lines are coincident and there are infinitely many solutions.