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)