First, lets take the second equation and solve for x. So, we need to move the y to the right side of the equation giving is

x-y+y=1-x+y which becomes x=1-x+y

now you want to move all the x’s together so you get:

x+x=1-x+y+x giving you 2x=1+y

now you need to isolate x, so you get

(2x)/2=(1+y)/2 giving you x=(1+y)/2

now, you substitue this answer in for any x you see in the first equation. Thus, you have:

(1+y)/2 +y=3((1+y)/2)-1

now, you need to solve the equation. first, lets multiply both sides by 2 to get rid of the fractions, leaving you with

1+y+y=3(1+y)-2

now lets distribute the 3 giving:

1+y+y=3+3y-2

group like terms, giving you:

1+2y=1+3y

now, we’ll move the variables to the same side of the eqution:

1+2y-3y=1+3y-3y giving you 1-y=1

now move the numerals to the same side, giving:

-y=0 thus y=0

Now, lets input the value for y into the second equation, in simplified form, to solve for x. Remember we had:

x=(1+y)/2

so we end up with x=(1+0)/2

this simplifies down to x=1/2

The FINAL step is to input both values into your equation and make sure it’s correct. So we have

x+y=3x-1 this gives us 1/2+0=3(1/2)-1

distribute the 3 to give you 1/2+0=3/2-1

now just do the addition and subtraction, leaving you with 1/2=1/2