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).