Question

The reason for the equations $x+2y=5$ and $4x+8y=20$ to have infinite solutions is

• A. The graph of the system of equations meets at infinity
• B. The graph reaches infinity
• C. The graph of both the equations is the same line
• D. none of these

Answer 1

The correct option is C

The graph of both the equations is the same line

On sketching the graph , we get the same line . In the line $4x+8y=20$, if we take the common factor 4 out , we get $x+2y=5$ which is same as the other line.So these lines are coincident and therefore have infinite points of intersections(solutions)