Question

2x+3y=9
3x+2y=11
Система линейного уравнения

Answer 1

$\left \{ {{2x+3y=9} \atop {3x+2y=11}} \right.\\\\\left \{ {{2x=9-3y} \atop {3x=11-2y}} \right.\\\\\left \{ {{2x=9-3y|*3} \atop {3x=11-2y|*2}} \right. \\\\\left \{ {{6x=27-9y} \atop {6x=22-4y}} \right. \\\\\left \{ {{6x=27-9y} \atop {27-9y=22-4y}} \right. \\\\\left \{ {{6x=27-9y} \atop {-9y+4y=22-27}} \right.\\\\\left \{ {{6x=27-9y} \atop {-5y=-5}}$

$\left \{ {{6x=27-9y} \atop {y=-5:(-5)}} \right. \\\\\left \{ {{6x=27-9y} \atop {y=1}} \right.\\\\\left \{ {{6x=27-9*1} \atop {y=1}} \right.\\\\\left \{ {{6x=27-9} \atop {y=1}} \right.\\\\\left \{ {{6x=18} \atop {y=1}} \right.\\\\\left \{ {{x=18:6} \atop {y=1}} \right.\\\\\left \{ {{x=3} \atop {y=1}} \right.$

Проверка:

$\left \{ {{x=3} \atop {y=1}} \right. \\\\\left \{ {{2x+3y=9} \atop {3x+2y=11}} \right. \\\\\left \{ {{2*3+3*1=9} \atop {3*3+2*1=11}} \right. \\\\\left \{ {{6+3=9} \atop {9+2=11}} \right. \\\\\left \{ {{9=9} \atop {11=11}} \right.$