Question

consider a system of two linear equations and two unknowns.
part a
if both equations are graphed and the system has no solution, describe the resulting graph. explain your reasoning.

Explanation:

A system of two linear equations with no solution means the equations represent parallel lines. Parallel lines have the same slope but different y - intercepts, so they never intersect (and an intersection point is the solution of the system). So the graph will show two distinct straight lines that are parallel to each other.

Answer:

The graph will consist of two distinct, parallel straight lines. This is because a system of two linear equations with no solution means the two lines representing the equations never intersect, and the only way two linear graphs (lines) never intersect is if they are parallel (same slope, different y - intercepts).