4x-y=3 and 3x-2y=1. Solve these simultaneous equations to find values for x and y.

Equation 1: 4x-y=3  Equation 2: 3x-2y=1

We have to find a common multiple between 4 and 3 so that both equations have the same first value. This means that we can get rid of the x by subtracting the second equation from the first. This will leave us with a simple linear equation with which we can solve to find y and then go on to find x. The lowest common denominator between 4 and 3 is 12. 

3(4x-y)=3x3 -> 12x-3y=9 (Eq. 1)
4(3x-2y)=4x1 -> 12x-8y=4 (Eq. 2)

Eq. 1 - Eq.2 = 12x-12x-3y--8y=9-4 ->  5y=5

hence y=1 and now we have to input the y value into the first (or second) equation to find x

4x-1=3 -> 4x=4 -> x=1

So x=1 and y=1