If [40/(x+y)] + [2/(x-y)] = 5 ; [25/(x+y)] - [3/(x-y)] = 1 ; what is the value of x and y?

Question

Find the value of x and y if

[40/(x+y)] + [2/(x-y)] = 5
[25/(x+y)] - [3/(x-y)] = 1

Answer 1

Simplify [40/(x+y)]+[2/(x-y)]=5..............................................(a)
=>5(x+y)(x-y)=42x-38y...........................................(i)
Simplify [25/(x+y)]-[3/(x-y)]=1...............................................(b)
=>[(x+y)(x-y)]=22x-28y...............................................(ii)
Now,put value of [(x+y)(x-y)] from (ii) to (i)
=>5[22x-28y]=42x-38y
=>x=1.5y..................................................................(iii)
Now,
Put value of x from (iii) into (a)
=>y=4 & x=6
Ans :x=6 & y=4

Answer 2

Let 1/(x+y) = a & 1/(x-y) = b
We get
40a +2b = 5 ----- eqn I
25a - 3b = 1 ----- eqn II

Solving these pair of linear equations in two variables, we get
a = 1/10, b = 1/2
or
x + y = 10 ----- eqn III
x - y = 2 ----- eqn IV

Again solving for x & y,
We get x = 6 & y = 4