Question

Показать,что система уравнений имеет бесконечное множество решений. Помогите пожалуйста ​

Answer 1

1)

$\displaystyle \tt \left \{ {{x+y=0} \atop {2x+2y=0}} \right. \to \left \{ {{x=-y} \atop {2x+2y=0}} \right. \\\\\displaystyle \tt 2\cdot(-y)+2y=0\\\displaystyle \tt -2y+2y=0\\\displaystyle \tt 0=0 \\\displaystyle \tt y \in \infty$

2)

$\displaystyle \tt \left \{ {{x-y=3} \atop {2x-2y=6}} \right. \to \left \{ {{x=3+y} \atop {2x-2y=6}} \right. \\\\\displaystyle \tt 2(3+y)-2y=6\\\displaystyle \tt 6+2y-2y=6\\\displaystyle \tt 6=6\\\displaystyle \tt y \in \infty$

3)

$\displaystyle \tt \left \{ {{2x-3y=1} \atop {4x-6y=2}\:\:\:\:|\div(-2)} \right. \to \left \{ {{2x-3y=1} \atop {-2x+3y=-1}} \right. \\\\\displaystyle \tt 0=0\\\displaystyle \tt y\in \infty$