{x+2y =6
{3x²-xy +4y²= 48
{x= 6-2y
{3x²-xy +4y²=48
3(6-2у)² - у(6-2у) +4у²=48
3(36- 24у+4у²) -6у+2у²+4у²-48=0
108 - 72у + 12у² -6у +6у²-48=0
18у² - 78у +60=0 |:2
9у²-39у+30=0
D= (-39)² -4*9*30 = 1521-1080= 441= 21²
y₁= (39-21)/ (2*9) = 18/18 =1
y₂= (39+21)/18 = 60/18= 10/3 = 3 1/3
x₁= 6-2*1=4
x₂= 6 - 2 * 3 1/3 = 6 - (2*10)/(1*3) = 6 - 6 2/3 = -2/3
Ответ : (4;1) , (-2/3 ; 3 1/3)