Question

Найти решение системы уравнений:

Answer 1

y=4x-16
2x²-4x²+16x-24=0
2x²-16x+24=0
x²-8x+12=0
x1+x2=8 U x1*x2=12
x1=2⇒y1=8-16=-8
x2=6⇒y2=24-16=8
(2;-8);(6;8)

Answer 2

$2 x^{2} -xy=24 \\ 4x-y=16\\ y=4x-16 \\ \\ 2 x^{2} -x(4x-16)=24\\ 2 x^{2} -4 x^{2} +16x-24=0\\ -2 x^{2} +16x-24=0/*(-1)\\ 2 x^{2} -16x+24=0/:2\\ x^{2} -8x+12=0\\D=64-4*12=64-48=16 \\ \sqrt{D} =4\\ x_{1} = \frac{8+4}{2} = \frac{12}{2} =6 \\ x_{2} = \frac{8-4}{2} = \frac{4}{2} =2$

$y_{1} =4*6-16=24-16=8 \\ y _{2} =4*2-16=8-16=-8\\ \\ \\ \left \{ {{y=8} \atop {x=6}} \right. \left \{ {{y=-8} \atop {x=2}} \right.$