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