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:

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

• For the Blue graphs: The two lines are vertical (parallel, since vertical lines have an undefined slope and are parallel if they have different x - intercepts). They will never intersect, so the system has no solution.
• For the Green graph: The two lines (wait, actually it's one line? No, looking at the Green graph, it's a single line? Wait, no, the Green graph shows a single line? Wait, no, the problem is about two linear equations, so two lines. Wait, the Green graph: if it's two lines? Wait, no, the Blue has two vertical lines, Green has one line? Wait, no, maybe the Green is two lines? Wait, no, the Blue: two vertical lines (parallel, so no intersection). Green: if it's two lines, they intersect (since it's a straight line with a slope, so two lines would intersect if they are not parallel). Pink: two lines that intersect (so they have a solution). So the Blue graphs represent two parallel lines (vertical), so no solution.

Answer:

A. Blue