Решите систему уравнение 1)2xy-x=7 x-5y=2 2)2x^2-xy=33 4x-y=17 3)x^2+2y=18 3x=2y

Question

Решите систему уравнение 1)2xy-x=7 x-5y=2

2)2x^2-xy=33 4x-y=17

3)x^2+2y=18

3x=2y

Answer 1

1) x=5y+2
2(5y+2)-y=7
10y+4-y=7
9y=3
y=1/3 ===> x= 5*1/3=5/3

 3)x^2+3x=18
x^2+3x-18=0
D=9-4*(-18)=9+72=81
x(1)=(-3+9)/2 => x(1)=3.5 => y(1) => 3*3.5 =2y =>y(1)= 5.25 

x(2)=(-3-9)/2 => x(2)=-6 => y(2) => 3*(-6)=2y => y(2)=-9

2) y=4x-17
2x^2-x(4x-17)=33
2x^2-4x^2-17x-33=0
-2x^2-17x-33=0
D=  289 - 4*(-2)*(-33) =289 - 264 = 25
x(1)= (17+5)/-4 = -5.5 => y(1) = 4*(-5.5)-17 => y(1)=-39
x(2)= (17-5)/-4=  -3 => y(2)= 4*(-3)-17 => y(2)=-29