Question

solve for x and y 2/x+2/3y=1/6 and 2/x-1/y=1​

Answer 1

$\frac{2}{x} + \frac{2}{3y} = \frac{1}{6} - eq(1) \\ \\ \frac{2}{x} - \frac{1}{y} = 1 - eq(2) \\ \\ subtracting \: eq(1) \: and \: eq(2) \\ \\ \: \: \frac{2}{x} + \frac{2}{3y} = \frac{1}{6} \\ \\ \: \: \: \frac{2}{x} - \frac{1}{y} = 1 \\ ( - ) \: \: ( + ) \: \: \: ( - ) \\ \\ - - - - - - - - - \\ \\ = > \frac{2}{3y} + \frac{1}{y} = 1 \\ \\ = > \frac{2 + 3}{3y} = 1 \\ \\ = > 5 = 3y = > y = \frac{5}{3} \\ \\ subtituting \: y \: value \: in \: eq(2) \\ \\ = > \frac{2}{x} - \frac{1}{ \frac{5}{3} } = 1 \\ \\ = > \frac{2}{x } - \frac{3}{5} = 1 \\ \\ = > \frac{2}{x} = 1 + \frac{3}{5} = \frac{8}{5} \\ \\ = > 10 = 8x \\ \\ = >x = \frac{5}{4}$