Question

Solve for x and y:
${\displaystyle \frac{9}{x}-\frac{4}{y}=8,\frac{13}{x}+\frac{7}{y}=101}$

Answer 1

The given equations are:
${\displaystyle \frac{9}{x}-\frac{4}{y}=8}$    ……..(i)
${\displaystyle \frac{13}{x}+\frac{7}{y}=101}$ ……..(ii)
Putting ${\displaystyle \frac{1}{x}=u\text{and}\frac{1}{y}}$= v, we get:
9u - 4v = 8 …….(iii)
13u + 7v = 101 ……(iv)
On multiplying (iii) by 7 and (iv) by 4, we get:
63u - 28v = 56 ……..(v)
52u + 28v = 404 ……..(vi)
On adding (v) from (vi), we get:
115u = 460 ⇒ u = 4
⇒${\displaystyle \frac{1}{x}=4\Rightarrow x=\frac{1}{4}}$
On substituting x =${\displaystyle \frac{1}{4}}$ in (i), we get:
${\displaystyle \frac{9}{1⁄4}-\frac{4}{y}=8}$
⇒${\displaystyle 36-\frac{4}{y}=8\Rightarrow \frac{4}{y}=(36–8)=28}$
y = ${\displaystyle \frac{4}{28}=\frac{1}{7}}$
Hence, the required solution is x = ${\displaystyle \frac{1}{4}\text{and}y=\frac{1}{7}}$.