Question

розпишіть способом підстановки рівнянь

Answer 1

Объяснение:

$\left \{ {{x-2y=5} \atop {3x+5y=26}} \right. \\\left \{ {{x=5+2y} \atop {3x+5y=26}} \right. \\\\\left \{ {{x=5+2y} \atop {3(5+2y)+5y=26}} \right.$

Решим второе уравнение системы:

$3*(5+2y) + 5y = 26\\15 + 6y + 5y = 26\\6y+5y = 26-15\\11y = 11\\y = 11:11\\y=1$

$\left \{ {{x=5+2y} \atop {y=1}} \right. \\\\\left \{ {{x=5+2*1} \atop {y=1}} \right. \\\\\left \{ {{x=7} \atop {y=1}} \right.$

Ответ: (7;1)

______________

$\left \{ {{3x+4y=55} \atop {7x-y=56}} \right. \\\\\left \{ {{3x+4y=55} \atop {y=7x-56}} \right. \\\\\left \{ {{3x+4(7x-56)=55} \atop {y=7x-56}} \right.$

Решим первое уравнение системы:

$3x+4(7x-56)=55\\3x + 28x - 224 = 55\\3x+28x = 55+224\\31x = 279\\x = 279:31\\x = 9$

$\left \{ {{x=9} \atop {y=7x-56}} \right. \\\\\\\left \{ {{x=9} \atop {y=7*9-56}} \right. \\\\\\\left \{ {{x=9} \atop {y=7}} \right.$

Ответ: (9;7)