Question

Розв'язати систему рівнянь методом підстановки 2. f 2х + Зу =12 6x - 5y = 8 0,2x - 4y = 2 0,5x+2y =11​

Answer 1

$\displaystyle\bf\\1)\\\\\left \{ {{0,2x-4y=2} |\cdot 5\atop {0,5x+2y=11}} \right. \\\\\\\left \{ {{x-20y=10} \atop {0,5x+2y=11}} \right\\\\\\\left \{ {{x=20y+10} \atop {0,5\cdot(20y+10)+2y=11}} \right\\\\\\\left \{ {{x=20y+10} \atop {10y+5+2y=11}} \right\\\\\\\left \{ {{x=20y+10} \atop {12y=6}} \right\\\\\\\left \{ {{x=20\cdot 0,5+10} \atop {y=0,5}} \right\\\\\\\left \{ {{x=20} \atop {y=0,5}} \right. \\\\\\Otvet \ : \ (20 \ ; \ 0,5)$

$\displaystyle\bf\\2)\\\\\left \{ {{2x+3y=12} \ |:2 \atop {6x-5y=8}} \right.\\\\\\\left \{ {{x+1,5y=6} \atop {6x-5y=8}} \right. \\\\\\\left \{ {{x=6-1,5y} \atop {6\cdot(6-1,5y)-5y=8}} \right.\\\\\\\left \{ {{x=6-1,5y} \atop {36-9y-5y=8}} \right. \\\\\\\left \{ {{x=6-1,5y} \atop {36-14y=8}} \right.\\\\\\\left \{ {{x=6-1,5y} \atop {14y=36-8}} \right. \\\\\\\left \{ {{x=6-1,5y} \atop {14y=28}} \right.\\\\\\\left \{ {{x=6-1,5\cdot 2} \atop {y=2}} \right.$

$\displaystyle\bf\\\left \{ {{x=3} \atop {y=2}} \right.\\\\\\Otvet \ : \ (3 \ ; \ 2)$