Question

Решите систему уравнений способом подстановки: 1){x/4+y/8=2, 2x/9+y/6=1; 2){7x/3-y/9=4, 8x/5-y/30=3

Answer 1

первая система: $left { {{ frac{x}{4}+ frac{y}{8} =2 } atop { frac{2x}{9}+ frac{y}{6}= 1}} right. \ left { {{2x+y=16} atop {4x+3y=18}} right. \ left { {{y=16-2x} atop {4x+3(16-2x)=18}} right. \ 4x+3(16-2x)=18 \ 4x+48-8x=18 \ 4x-8x=18-48 \ -4x=-30 \ x=7.5 \ left { {{y=16-2x} atop {x=7.5}} right. \ left { {{y=16-2*7.5} atop {x=7.5}} right. \ left { {{y=1} atop {x=7.5}} right.$
вторая система: $left { {{ frac{7x}{3}- frac{y}{9}=4 } atop { frac{8x}{5}- frac{y}{30}=3 }} right. \ left { {{21x-y=36} atop {48x-y=90}} right. \ left { {{y=21x-36} atop {48x-(21x-36)=90}} right. \ 48x-(21x-36)=90 \ 48x-21x+36=90 \ 27x=90-36 \ 27x=54 \ x=2 \ left { {{y=21x-36} atop {x=2}} right. \ left { {{y=21*2-36} atop {x=2}} right. \ left { {{y=42-36} atop {x=2}} right. \ left { {{y=6} atop {x=2}} right.$