What is the solution to the system of 4x-3y=1 and y+2x=3?

Use substitution, so subtract 2x from both sides of the second equation, leaving y by itself, so y=3-2x, or -2x+3. Then you have these two equations, y=-2x+3 and 4x-3y=1. Substitute -2x+3 for the y, giving the equation 4x-3(-2x+3) =1. Then you distribute and get 4x+6x-9=1. Combine like terms, and you're left wide 10x-9=1. Add nine, and you get 10x=10, so x=1