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

1 Answer
mason m
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 #(3,-2)#.

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