Question

x/2+y/3=1

4y-3x=2

Answer 1

x/2+y/3=1

4y-3x=2

It is less error-prone to work with integral coefficients, so multiply the first equation by 6 (common denominator), and to arrange the x and y in alphabetic order:

3x+2y=6 ...(1)
-3x+4y=2...(2)

Here it is obvious that we can eliminate x simply by adding (1) and (2):
3x-3x+2y+4y=6+2
6y=8
y=4/3
Substitute y in (1):
3x+2(4/3)=6
3x = 6-8/3
x=(10/3)/3
=10/9

or x=10/9, y=4/3

Check (using the original equations):
From (1)
x/2+y/3=1
(10/9)/2+(4/3)/3
=5/9+4/9
=1

From (2)
4y-3x=2
4(4/3)-3(10/9)
=2
So the solution is correct.