A system of two linear equations is graphed on a coordinate plane. if the system of equations has infinitely many solutions, which statement must be true?

Question

A
On the graph, there are no points (x,y)\left(x,y\right)(x,y) that satisfy both equations.
B
On the graph, there is exactly one point (x,y)\left(x,y\right)(x,y) that satisfies both the equations.
C
On the graph, any point (x,y)\left(x,y\right)(x,y) that satisfies one of the equations cannot satisfy the other equation.
D
On the graph, any point (x,y)\left(x,y\right)(x,y) that satisfies one of the equations must also satisfy the other equation.

Answer 1

If a system of two linear equations has infinitely many solutions, it means that the two equations represent the same line on the coordinate plane. Therefore, any point that lies on one line will also lie on the other line.

Based on this understanding, the correct statement is:

D: On the graph, any point (x,y) that satisfies one of the equations must also satisfy the other equation.

This is because if the two equations are equivalent (as they must be for there to be infinitely many solutions), then all points along the line are solutions for both equations.