8/3x-2 + 45/4y+3=5 a and 12/3x-2 - 30/4y+3 = 1
The solution is easier if we can spot that a simple substitution can be made.
Let u = 3x - 2 ams let v = 4y + 3, then our equations become
8/u + 45/v = 5
12/u - 30/v = 1
Multiplying both equations by uv gives us,
8v + 45u = 5uv
12v - 30u = uv
multiply 2nd equation by 5
8v + 45u = 5uv
60v - 150u = 5uv
subtract 1st eqn from the 2nd,
52v - 195u = 0
u = (52/195)v = (4/15)v
Substituting for u = (4/15)v into the very first of the two eqns above, viz. 8v + 45u = 5uv, then
8v + 45(4/15)v = 5(4/15)v^2
8v + 12v = (4/3)v^2
60v = 4v^2
v^2 - 15v = 0
v(v - 15) = 0
v = 0, v = 15
Since v is used as a denominator, then we must ignore the solution v = 0, leaving us with but one solution, v = 15
Hence, u = 4, and v = 15
From which, x = 2, y = 3