Solve: 11/x-7/y=1 and 9/x-4/y=6
$\frac{11}{x} – \frac{7}{y} = 1$ —-(i)
$\frac{9}{x} – \frac{4}{y} = 6$ —-(ii)
Let, $\frac{1}{x}$ =u and $\frac{1}{y}$=v
Then Equations (i) and (ii) can be written as-
11u-7v=1 —(iii)
and 9u -4v=6 —(iv)
Multiplying equation (iii) by 4 and equation (iv) by 7 we get,
44u-28v=4 —(v)
63u-28v=42 —(vi)
Subtracting Equation (v) from (vi) we get,
(63u-28v)-(44u-28v)=42-4
⇒ 63u-28v-44u+28v = 38
⇒ 19u = 38
⇒ u=$\frac{38}{19}$
⇒ u = 2
Substituting the value of u in equation (iii) we get,
11u-7v=1
⇒ 11(2)-7v=1
⇒ 22 -7v=1
⇒ 22-1=7v
⇒ 21 =7v
⇒ v= $\frac{21}{7}$
⇒ v= 3
∴ u = 2 and v = 3
∴ x = $\frac{1}{2}$ and y=$\frac{1}{3}$