Question

solve for x and y : 11/x-7/y=1, 9/x-4/y=6​

Answer 1

and that's your answer

Answer 2

Let $\frac{1}{x}$ be u and $\frac{1}{y}$ be v.

$11u - 7v = 1 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: ...(1) \\ \\ 9u - 4v = 6 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: ...(2)$

From equation 1 :

$11u - 7v = 1 \\ \\ 11u = 1 + 7v \\ \\ \bf u = \frac{1 + 7u}{11}$

Substituting the value of u in equation 2 we get :

$9( \frac{1 + 7v}{11} ) - 4v = 6 \\ \\ \frac{9 + 63v}{11} - 4v = 6 \\ \\ \frac{9 + 63v - 44v}{11} = 6 \\ \\ \frac{9 + 19v}{11} = 6 \\ \\ 9 + 19v = 66 \\ \\ 19v = 66 - 9 \\ \\ 19v = 57 \\ \\ v = \frac{57}{19} \\ \\ \bf v = 3$

Putting the value of v in equation 1 we get :

$11u - 7(3) = 1 \\ \\ 11u - 21 = 1 \\ \\ 11u = 1 + 21 \\ \\ 11u = 22 \\ \\ u = \frac{22}{11} \\ \\ \bf u = 2$

Now,

$\frac{1}{x} = u \\ \\ \frac{1}{x} = 2 \\ \\ \bf x = \frac{1}{2} \\ \\ \bf and \\ \\ \frac{1}{y} = v \\ \\ \frac{1}{y} = 3 \\ \\ \bf y = \frac{1}{3}$

Hope it helps! ;)