Question

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?
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. Therefore, any point that satisfies one equation will also satisfy the other.

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 indicates that the two lines are coincident, leading to infinitely many solutions.