Question

1/2(3x+4y)+1/5(2x-3y)=1/4;5(3x+4y)-2(2x-3y)=-3/2

Answer 1

Let 1/(3x+4y)=a & 1/(2x-3y)=b
So a/2+b/5=1/4
(5a+2b)/10=1/4
10a+4b=5---------------------(1)
5a-2b=-3/2
10a-4b=-3---------------------(2)
Eq(1)+eq(2)
20a=2
a=1/10
Put a in eq 1
1+4b=5
b=1
Now
1/(3x+4y)=1/10
3x+4y=10----------------------(3)
Also 1/(2x-3y)=1
2x-3y=1---------------------------(4)
2eq(3)-3eq(4)
6x+8y-6x+9y=20-3
17y=17
y=1
Put y in eq 3
3x+4=10
x=2