Question

4. сколько решений имеет система уравнений:
y=x² - 2х -3,
у = -3​

Answer 1

Два решения :

$\left \{ {{y=x^{2} -2x-3} \atop {y=-3}} \right.\\\\\left \{ {{-3=x^{2}-2x-3 } \atop {y=-3}} \right.\\\\\left \{ {{x^{2}-2x=0 } \atop {y=-3}} \right.\\\\\left \{ {{x(x-2)=0} \atop {y=-3}} \right.\\\\\left \{ {{\left[\begin{array}{ccc}x_{1}=0 \\x_{2}=2 \end{array}\right} \atop {y=-3}} \right. \\\\Otvet:\boxed{(0;-3),(2;-3)}$

Answer 2

$\left \{ {{y=x^{2} -2x -3} \atop {y=-3}} \right. \\x^{2} -2x-3 = -3\\ x^{2} -2x = 0\\x(x-2) = 0\\x= 0; x=2\\ (x1, y1) = (0; -3)\\(x2, y2) = (2; -3)$