​ Solve the following systems of equations: 22/(x+y) + 15/(x - y) = 5 55/(x+y) + 45/(x - y) = 14 ​

Question

Solve the following systems of equations:

\(\frac{22}{x+y}\)+\(\frac{15}{x-y}\) = 5

\(\frac{55}{x+y}\)+\(\frac{45}{x-y}\) = 14

Answer 1

 \(\frac{22}{x+y}\)+\(\frac{15}{x-y}\) = 5

\(\frac{55}{x+y}\)+\(\frac{45}{x-y}\) = 14

Multiplying eq1 by 3 and subtracting from eq2

⇒ - 11/(x + y) = - 1

⇒ x + y = 11 ---------- (3)

Multiplying eq1 by 5 and eq2 by 2 and subtracting

⇒ 15/(x – y) = 3

⇒ x – y = 5 ------ (4)

(3) + (4)

⇒ 2x = 16

⇒ x = 8

Thus,

y = 3