Question

решите систему
1)x=y+2
3x-2y=9
2)x=2y-3
3x+2y=7
3)y=3-x
x+2y=3
4)x=4y
x+5y=99
5)y=-4x
x-y=10​

Answer 1

$1)left { {{x=y+2} atop {3x-2y = 9}} right. \\ 3(y+2) - 2y = 9\\3y + 6 - 2y = 9\\3y - 2y = 9-6\\y = 3\\x = y + 2 = 3+2 = 5$

Ответ: (5; 3)

$2) left { {{x=2y - 3} atop {3x+2y = 7}} right. \\ 3(2y - 3) + 2y = 7\\6y - 9 + 2y = 7\\6y + 2y = 7 + 9\\8y = 16\\y = 2\\x = 2cdot 2 - 3 = 4 - 3 = 1$

Ответ: (1; 2)

$3) left { {{y=3-x} atop {x+2y = 3}} right.\\x + 2(3-x) = 3\\x + 6 - 2x = 3\\x - 2x = 3-6\\-x = -3\\x = 3\\y = 3 -3 = 0$

Ответ: (3; 0)

$4) left { {{x = 4y} atop {x+5y=99}} right.\\4y + 5y = 99\\9y = 99\\y = 11\\x = 4cdot 11 = 44$

Ответ: (44; 11)

$5) left { {{y=-4x} atop {x-y=10}} right. \\x - (-4x) = 10\\ x + 4x = 10\\5x = 10\\x = 2\\y = (-4)cdot 2 = -8$

Ответ: (2; -8)