Describe 3 ways that two lines can intersect. What is true about the slopes of the lines in each of the 3 examples of two equation systems? What can you expect to happen if you solve each type of the system algebraically?
I think your question needs to be a little more specific, but I will try to give you the best answer possible.
1. Two lines can intersect and be perpendicular to each other. This will make their slopes negative reciprocals of each other. In an algebraic system, you would find that one would equal (y1-y) = m(x1-x) while the other would equal (y1-y) = (-1/m)(x1-x) with (x.y) being the point at which they intersect.
2. The two lines can be intersecting, without their lines being perpendicular or parallel. This will give you two different, non negative reciprocal slopes and your algebraic systems would be distinct from each other.
3. If two algebraic systems occupy the same line, this means that they are intersecting each other at every single point. The slopes would therefore be the same and because they are also the same line, the algebraic systems will be identical when simplified down.