graphing a linear equation

Question

can you determine how many  solutions 2 equations has without graphing 

Answer 1

Yes

 

You will have one of three possibilities as follows:

 

1. The typical solution, where two lines intersect at just one point.  You will know this because they are distinct lines, with different slopes.  In y=mx+b form, m would be different.  If solving, you will get a distinct x,y point.
2. Parallel lines, which will never meet (no solution).  If your slopes are the same, but the y intercept is different, they are parallel.  If solving, you will get an incorrect statement like 5=10.
3. Coincident lines, which have an infinite solution, as they are indeed the same line.  If you solve for y=mx+b, they will be identical.  If you solve for x,y, you may lose x, but get a true statement like 5=5.