Question

Решите систему уравнения
{1/3х+1/5у=11
{3/5х-2у=8

Answer 1

$left { {{ frac{1}{3}x+ frac{1}{5}y=11}atop{ frac{3}{5}x-2y =8}} right.$

$left { {{ frac{1}{3}x*10+ frac{1}{5}*10 =11*10} atop { frac{3}{5} =8}} right.$⇒$left { {{ frac{10}{3}x+2y=110} atop { frac{3}{5}x-2y =8}} right.$
$frac{10}{3}x+ frac{3}{5}x=118$

$frac{10*5}{3*5}x+ frac{3*3}{5*3}x=118$

$frac{50+9}{15}x=118$

$frac{59}{15}x=118$
$x=118: frac{59}{15}$
$x=118* frac{15}{59}$
$x=30$

$frac{10}{3}*30+2y=110$
$100+2y=110$
$2y=110-100$
$2y=10$
$y=5$

Проверка:$left { {{ frac{1}{3}*30+ frac{1}{5}*5 =11} atop { frac{3}{5}*30-2*5 =8}} right.$⇒$left { {{10+1=11} atop {18-10=8}} right.$
Ответ:x=30; y=5