Question

solve the following air of equation for x and y 15by x-y +22by x+y =5 and 40by x-y +55by x+y =13(x not equal to y, x not equal to -y)

Answer 1

Let 1/(x-y)=a & 1/(x+y)=b
So eqns are as follows
15a+22b=5--------------------(1)
40a+55b=13-------------------(2)
5eq(1)-2eq(2)
75a+110b-80a-110b=25-26
-5a=-1
a=1/5
Put a in eq(1)
3+22b=5
22b=2
b=1/11
So according to our assumption
1/(x-y)=1/5
x-y=5---------------------(3)
1/(x+y)=1/11
x+y=11---------------------(4)
Eq(3)+eq(4)
2x=16
x=8
Put x in eq(3)
y=3