Describe the graphs of the following linear system of equations: One solution


No solution

Infinite solutions

What have you learned about the slopes and y-intercepts of each of these linear systems of equations?

One solution:

The lines only intersect in one place.

No solution:

This means the lines never meet. The only way this is possible is if the lines are parallel. Actually, that's literally the definition: parallel lines never meet.

Infinite solutions:

The lines are one. They overlap completely, that's why all the points on the lines are shared.

And as for what you've learned, I can't help you there. But:

-lines with the same slope are always parallel-- unless the y-intercept is also the same, then they are the same line.

-if the slopes of two lines are opposite reciprocals, they will meet at exactly one point, and they are perpendicular.

hmm, those are the only two things I can think of at the moment. Hope I could help you!

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