​ Solve the following systems of equations: 3/(x+y) + 2/(x - y) = 2 9/(x+y) - 4/(x - y) = 1 ​

Question

Solve the following systems of equations:

\(\frac{3}{x+y}\)+\(\frac{2}{x-y}\)= 2

\(\frac{9}{x+y}\) - \(\frac{4}{x-y}\) = 1

Answer 1

 \(\frac{3}{x+y}\)+\(\frac{2}{x-y}\)= 2

\(\frac{9}{x+y}\) - \(\frac{4}{x-y}\) = 1

Multiplying eq1 by 2 and adding to eq2

⇒ 15/(x + y) = 5

⇒ x + y = 3 ------- (3)

Multiplying eq1 by 3 and subtracting eq2 from it

⇒ 10/(x – y) = 5

⇒ x – y = 2 ---- (4)

Adding the two equation

⇒ 2x = 5

⇒ x = 5/2

Thus,

y = 1/2