Question

Решите систему уравнений:
1. а) x-3y=-1 б)2x^2-5y=27
xy+4y=18 2x-y=7

Answer 1

а)

$\left \{ {{x-3y=-1} \atop {xy+4y=18}} \right.;\\x=3y-1\\(3y-1)y+4y=18\\3y^2+3y-18=0\\D=9+12*18=225\\y=\frac{-3б15}{6}=\left[\begin{array}{ccc}-3\\2\\\end{array}$

$\left[\begin{array}{ccc}\left \{ {{y=-3} \atop {x-3*(-3)=-1=>x=-10}} \right. \\\left \{ {{y=2} \atop {x-3*2=-1=>x=5}} \right. \\\end{array}$

Ответ: (-10;-3) и (5;2)

б)

$\left \{ {{2x^2-5y=27} \atop {2x-y=7}} \right.\\y=2x-7=>5y=10x-35\\2x^2-10x+35-27=0\\x^2-5x+4=0\\D=25-16=3^2\\x=\frac{5б3}{2}=\left[\begin{array}{ccc}1\\4\\\end{array}$

$\left[\begin{array}{ccc}\left \{ {{x=1} \atop {2*1-y=7=>y=-5}} \right. \\\left \{ {{x=4} \atop {2*4-y=7=>y=1}} \right. \\\end{array}$

Ответ: (1;-5) и (4;1)