Question

9 you are solving a system of two linear equations in two variables, and you discover that there is no solution to the system. which of the following graphs could be the system your were solving? blue green pink a blue b green c pink

Explanation:

Step1: Recall solution conditions for linear systems

A system of two linear equations in two variables has no solution when the lines are parallel (same slope, different y - intercepts), as parallel lines never intersect.

Step2: Analyze each graph

• Blue Graph: The two lines are vertical (parallel, since vertical lines have an undefined slope and are parallel if they have different x - intercepts). So they will never intersect, meaning no solution.
• Green Graph: The two lines (wait, actually, looking at the Green graph, it's a single line? Wait, no, the problem says a system of two linear equations. Wait, maybe the Green graph has two lines? Wait, no, the Blue graph has two vertical lines, Green graph: let's see, the Green graph - if it's two lines, they have different slopes (one is a line with negative slope, and if there were two lines, but maybe the Green graph has two intersecting lines? Wait, no, the Blue graph: two vertical lines (parallel), Green: maybe two lines with different slopes (so they intersect, so one solution), Pink: two lines with the same slope? Wait, no, Pink graph: the two lines seem to intersect, so they have different slopes? Wait, no, the Pink graph: the two lines are not parallel, so they intersect (one solution). The Blue graph: two vertical lines (parallel, same slope (undefined), different x - intercepts), so no solution.

Answer:

A. Blue