​ Solve each of the following systems of equations by the method of cross-multiplication: 5/(x+y) - 2/(x - y) = - 1 15/(x+y) + 7/(x - y) = 10

Question

Solve each of the following systems of equations by the method of cross-multiplication:

\(\frac{5}{x+y}\) - \(\frac{2}{x-y}\)= - 1

\(\frac{15}{x+y}\) + \(\frac{7}{x-y}\) = 10 where x ≠ 0 and y ≠ 0

Answer 1

Method of cross multiplication

a₁x + b₁y + c₁ = 0

a₂x + b₂y + c₂ = 0

Given,

 \(\frac{5}{x+y}\) - \(\frac{2}{x-y}\)= - 1

\(\frac{15}{x+y}\) + \(\frac{7}{x-y}\) = 10

Multiplying eq1 by 3 and subtracting from eq2

⇒ \(\frac{13}{x-y}\) = 13

⇒ x – y = 1 ------- (3)

Multiplying eq2 by 2 and eq1 by 7 and adding

⇒ 65/(x + y) = 13

⇒ x + y = 5 ---------- (4)

Thus,

⇒ x = 6/2 = 3 and y = 4/2 = 2