Question

3 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) that satisfy both equations.
b. On the graph, there is exactly one point (x, y) that satisfies both equations.
c. On the graph, any point (x, y) that satisfies one of the equations cannot satisfy the
other equation.
d.
On the graph, any point (x, y) that satisfies one of the equations must also satisfy
the other equation.

Answer 1

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

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If the system of linear equations has infinitely many solutions, it means the two lines overlap.

In other words, each point of one of the lines also belongs to the second line.

Choices a, b, c give us one or no solutions and therefore not the answer.

Choice d is reflecting the infinitely many solutions and hence is the correct one.