Question

Скільки розв'язків має система рівнянь y^2 - x^2 = 0, 2x + y = -3;

Answer 1

Ответ:

Система имеет 2 решения: (-1;-1),(-3;3)

Объяснение:

$\displaystyle \left \{ {{y^2-x^2=0} \atop {2x+y=-3}} \right. < = > \left \{ {{(-3-2x)^2-x^2=0} \atop {y=-3-2x}} \right. < = > \left \{ {{9+12x+4x^2-x^2=0|:3} \atop {y=-3-2x}} \right. < = > \left \{ {{x^2+4x+3=0} \atop {y=-3-2x}} \right. < = > \left \{ {{(x+1)(x+3)=0} \atop {y=-3-2x}} \right. < = > \left \{ {{\left[\begin{array}{ccc}x+1=0\\x+3=0\\\end{array}\right} \atop {y=-3-2x}} \right. < = >$

$\displaystyle < = > \left \{ {{\left[\begin{array}{ccc}x=-1\\x=-3\\\end{array}\right} \atop {{\left[\begin{array}{ccc}y=-3-2*(-1)\\y=-3-2*(-3)\\\end{array}\right} \right. < = > \left \{ {{\left[\begin{array}{ccc}x=-1\\x=-3\\\end{array}\right} \atop {{\left[\begin{array}{ccc}y=-3+2\\y=-3+6\\\end{array}\right} \right. < = > \left \{ {{\left[\begin{array}{ccc}x=-1\\x=-3\\\end{array}\right} \atop {{\left[\begin{array}{ccc}y=-1\\y=3\\\end{array}\right} \right.$