Question

Stefan wants to graph a system of two linear equations to find the solution. Which

statement about the graph of the system is true?
A. If the graph of the system shows parallel lines, then there are infinite
solutions.
B. If the graph of the system shows only one line, then there are infinite
solutions.
C. If the graph of the system shows perpendicular lines, then there are no
solutions.
O
D. If the graph of the system shows lines that cross through the origin, then
there are no solutions.

Answer 1

Answer: The correct answer is A. If the graph of the system shows parallel lines, then there are infinite solutions.

When two linear equations in the system have the same slope and different y-intercepts, the lines will be parallel and will never intersect. This means that there is no solution to the system.

On the other hand, when two linear equations in the system have different slopes, the lines will intersect at exactly one point, which is the unique solution to the system.

So, in summary:

Parallel lines: no solution

Intersecting lines: one solution

Infinite solutions: lines are the same.

Explanation: