Question

Solve the pair of equation by reducing them to a pair of linear equation.​

Answer 1

Answer:

$\frac{7x - 2y}{xy} = 5 \\ \frac{7x}{xy} - \frac{2y}{xy} = 5 \\ \frac{7}{y} - \frac{2}{x} = 5 \\ let \: \frac{1}{y} = b \: \: and \: \: \frac{1}{x} = a \\ 7b - 2a = 5 \\ \frac{8x + 7y}{xy} = 15 \\ \frac{8}{y} + \frac{7}{x} = 15 \\ 8b + 7a = 15 \\ 7b - 2a = 5 \\ 7b - 5 = 2a \\ \frac{7b - 5}{2} = a$

putting in equation 2

$8b + 7a = 15 \\ 8b + 7( \frac{7b - 5)}{2} = 15 \\ 16b + 49b - 35 = 15 \times 2 \\ 65b = 30 + 35 \\ 65b = 65 \\ b = 1 \\ a = \frac{7b - 5}{2} \\ a = 7 \times 1 - 5 \div 2 \\ a = \frac{2}{2} \\ a = 1$

but,

$a = \frac{1}{x} \: \: \: \: b = \frac{1}{y} \\ x = 1 \: \: \: y = 1$