to solve system of equations given such as y-3x=5 and y+x=3 we first want to isolate a variable in this case will use y (NOW you want to keep it easy so isolate y from the second equation not the second one) so y=3-x then we sub this equation into the second one whereever y appears because we know y=3-x so now we get

3-x-3x=5 now you expand -4x=2 rearrange and isolate x and get x=-1/2 now we solve for y

y+x=3 -1/2+x=3 y=3.5

then we verify by plugging into the second equation

3.5-3(-0.5)=5 3.5+1.5=5 5=5

now if you do it the other way such as x=3-y when you plug it into the other equation you have to multiply out the 3 so that y-3(3-y)=5 y-9+3y=5 4y=14 y=3.5

so you can isolate y or x and get the same answer.

Hope this helps if you need more just ask

in short

isolate a variable from one equation

sub it into the other equation then solve

take that and sub it into the first equation and solve

then verify your equations by plugging both variables (the numbers) in to the other equation

Here is a link to also help you: http://cstl.syr.edu/FIPSE/Algebra/Unit5/subst.htm