Question

Решите систему уравнений:
{ x − y/3 = 8/3
{−2(5x+y)+15x−7y=6

Answer 1

$\left \{ {{x -\frac{y}{3} = \frac{8}{3} } \atop {-2(5x+y)+15x-7y=6}} \right. \Rightarrow \left \{ {{3x-y=8} \atop {-10x-2y+15x-7y=6}} \right. \Rightarrow \left \{ {{3x-y=8} \atop {5x-9y=6}} \right.$
После упрощения решаем обычную систему
$\left \{ {{3x-y=8 \ \ \ \ (\cdot -9)} \atop {5x-9y=6}} \right. \\ +\left \{ {{-27x+9y=-72} \atop {5x-9y=6}} \right. \\ -27x+9y+5x-9y=-72+6 \\ -27x+5x=-72+6 \\ -22x=-66 \\ x = 3 \\ \\ 3x-y=8 \\ 9-y=8 \\ y = 1$