# How do you graph the linear system and tell how many solution it has for x+y=1 and 2x-3y=12?

Feb 15, 2016

The solutions of a linear system occur when the lines intersect. When we graph two lines, there are $3$ possible outcomes:

• The lines intersect at one point, which is the one solution.
• The lines are parallel and never intersect, yielding no solutions.
• The lines are the same line and have an infinite number.

Graph the two equations:

graph{(x+y-1)(2x-3y-12)=0 [-15.02, 17.02, -9.04, 6.98]}

There is one solution at $\left(3 , - 2\right)$.