​ Solve the following systems of equations: 1/{2(x+2y)} + 5/{3(3x - 2y)} = - 3/2 5/{4(x+2y)} - 4/{5(3x - 2y)} = 73/60

Question

Solve the following systems of equations:

\(\frac{1}{2(x+2y)}\)+\(\frac{5}{3(3x-2y)}\)= \(\frac{-3}{2}\)

\(\frac{5}{4(x+2y)}\) - \(\frac{4}{5(3x-2y)}\)= \(\frac{73}{60}\)

Answer 1

 \(\frac{1}{2(x+2y)}\)+\(\frac{5}{3(3x-2y)}\)= \(\frac{-3}{2}\)

\(\frac{5}{4(x+2y)}\) - \(\frac{4}{5(3x-2y)}\)= \(\frac{73}{60}\)

Multiplying eq1 by 5/2 and subtracting from eq2

⇒ 3x – 2y = - 1 ------- (3)

Multiplying eq1 by 12/25 and adding to eq2

⇒ x + 2y = 3 ------- (4)

Solving (3) and (4)

We get,

x = 1/2 and y = 5/4