Question

Solve for x and y $4x+\frac{6}{y}=15;6x-\frac{8}{y}=14$

Answer 1

$4x+\frac{6}{y}=15;6x-\frac{8}{y}=14$
Let $\frac{1}{y}=z$
$\therefore$ Equations become
4x+6z=15 ....(1)
6x-8z=14 ....(2)
Multiply (1) with 4 and with 3 we get,
$16x+\text{/}24x=60...\left(3\right)$
$\underset{–}{18x-\text{/}24z=42...\left(4\right)}$
$84x=102$
$\therefore x=\frac{102}{34}$
$\therefore x=3$
From (1), $4x+6z=15\Rightarrow z=\frac{15-4x}{6}$
$\therefore z=\frac{15-(4\times 3}{6}=\frac{15-12}{6}=\frac{3}{6}=\frac{1}{2}$
$z=\frac{1}{2}$
$y=\frac{1}{z}=2$
$\therefore y=2$
$x=3,y=2$