​ Solve the following systems of equations: 1/5x + 1/6y = 12 1/3x - 3/7y = 8, x ≠ 0, y ≠ 0 ​

Question

Solve the following systems of equations:

\(\frac{1}{5x}\)+\(\frac{1}{6y}\) = 12

\(\frac{1}{3x}\) - \(\frac{3}{7y}\) = 8, x ≠ 0, y ≠ 0

Answer 1

 \(\frac{1}{5x}\)+\(\frac{1}{6y}\) = 12

\(\frac{1}{3x}\) - \(\frac{3}{7y}\) = 8, x ≠ 0, y ≠ 0

Multiplying eq1 by 1/3 and eq2 by 1/5 and subtracting

⇒ 1/18y + 3/35y = 4 - 8/5

⇒ 89/630y = 12/5

⇒ y = 89/1512

Thus,

1/5x + 1512/534 = 12

⇒ 1/5x = 816/89

⇒ x = 89/4080