Question

7x+5y/ 4x-3y= 87/17 daca si numai daca x/y= 8/5

Answer 1

$\dfrac{7x+5y}{5x+3y}=\dfrac{87}{17}$
$\dfrac{x}{y}=\dfrac{8}{5}$
$\dfrac{x}{y}=\dfrac{8}{5} => x=8a ; y=5a$

$\dfrac{7x+5y}{4x-3y}=\dfrac{87}{17}$
$\dfrac{7\cdot8a+5\cdot5a}{4\cdot8a-3\cdot5a}=\dfrac{87}{17}$
$\dfrac{56a+25a}{32a+15a}=\dfrac{87}{17}$
$87(32a+15a)=17(56a+25a)$
$2784a+1305a=952a+425a$
$4089a=1377a$