Question

solve for x and y 3/x+y + 2/x-y​= 2
9/x+y - 4/x-y = 1

Answer 1

Answer:

x=5/2 , y=1/2

Step-by-step explanation:

Let 1/x+y = u, 1/x-y = v.

3/x+y + 2/x-y = 2

=> 3u + 2v = 2 ...(i)

9/x+y - 4/x-y = 1

=> 9u - 4v = 1 ...(ii)

(i)×2 + (ii)×1,

6u + 4v = 4

(+) 9u - 4v = 1

15u + 0 = 5

=> 15u = 5

=> u = 1/3

Substituting u=1/3 in equation (i),

3×1/3 + 2v = 2

=> 1 + 2v = 2

=> 2v = 2 - 1

=> v = 1/2

So, 1/x+y = u and, 1/x-y = v

=> 1/x+y = 1/3 => 1/x-y = 1/2

=> x+y = 3 ...(iii) => x-y = 2 ...(iv)

(iii) + (iv),

x + y = 3

(+) x - y = 2

2x+0= 5

=> 2x = 5

=> x = 5/2

Substituting x=5/2 in equation (iii),

5/2 + y = 3

=> y = 3 - 5/2

=> y = 6-5/2

=> y = 1/2

Hence, x=5/2 and y=1/2.