Show steps . i'd really appreciate it.

First, we should manipulate the equations so that they equal the same things, so that we can set them equal to each other. We have problem, since they both have multiple variables, so if we set the equations equal to a variable, we can cancel it out and solve for the one remaining.

Let's first start by solving for x. We need to set the equations equal to y.
4x+3y=1
3y=1-4x
y=(1-4x)/3

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

Now we can set them equal to each other.
(1-4x)/3=(2-3x)/2
2(1-4x)=3(2-3x)
2-8x=6-9x
x=4

We can do the opposite to find y.
4x+3y=1
4x=1-3y
x=(1-3y)/4

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

Now set them equal to each other and solve for y.
(1-3y)/4=(2-2y)/3
3(1-3y)=4(2-2y)
3-9y=8-8y
3-8=9y-8y
y= -5