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)

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

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)

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

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)