Question

Помогите мне! (задание на фото)

Answer 1

{2x-y=6
{2x²+y²=66

2x-y=6
-y=6-2x
 y=2x-6

2x²+(2x-6)²=66
2x²+4x²-24x+36-66=0
6x²-24x-30=0
 x²-4x-5=0
D=4²-4*(-5)=16+20=36
x₁=4-6= -1
       2
x₂=4+6=5
       2

При х=-1
у=2*(-1)-6=-8

При х=5
у=2*5-6=4

Ответ: х=-1     у=-8
           х=5      у=4

Answer 2

$\left \{ {{2x-y=6} \atop {2 x^{2} +y ^{2} =66}} \right. \\ y=2x-6\\2 x^{2} +(2x-6) ^{2} =66\\2 x^{2} +4 x^{2} +36-24x-66=0\\6 x^{2} -24x-30=0/:6\\ x^{2} -4x-5=0 \\ D=16+20=36\\ \sqrt{D} =6\\ x_{1} = \frac{4+6}{2} =5\\ x_{2} = \frac{4-6}{2} =-1\\y _{1} =10-6=4\\y _{2} =-2-6=-8 \\ \left \{ {{x=5} \atop {y=4}} \right. \left \{ {{x=-1} \atop {y=-8}} \right.$