Question

How do you determine whether a linear system has one solution, many solutions, or no solution when given y = x + 3 and y = –2x + 3?

Answer 1

This system has one solution. See explanation.

Explanation:

You can see that both equations show lines in the directional form, and their slopes are different, so those lines have exactly one common point. If you compare right sides you get:

`x+3=-2x+3`

`x=0`

Now if you substitute `x` in any of the equations you get: `y=3`. So the only solution is `(0;3)`.