Question

Решите систему с постановки

Answer 1

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Answer 2

Пошаговое объяснение:

$1)\left \{ {{\frac{x}{2}+\frac{y}{3}=3 } \atop {\frac{x}{3}+\frac{y}{2}=\frac{8}{3}}} \right.=\left \{ {{3x+2y=18} \atop {2x+3y=16}} \right.= \left \{ {{-6x-4y=-36} \atop {6x+9y=32}} \right.\\\\ -13y=-68\\13y=68\\y=\frac{68}{13}\\\\ 6x+9*\frac{68}{13}=32\\\\ 6x+\frac{612}{13}=32\\\\ 6x=32-\frac{612}{13}\\\\ 6x=\frac{416}{13}-\frac{612}{13} \\\\ 6x=-\frac{196}{13}\\\\ x=-\frac{196}{13} :6\\\\x=-\frac{196}{13}*\frac{1}{6}\\\\ x=-\frac{196}{78}\\\\ x=-\frac{98}{39}$

$2)\left \{ {{\frac{2x}{3}-\frac{5y}{4}=-3} \atop {\frac{5x}{6}+\frac{7y}{8}=6}} \right.=\left \{ {{8x-15y=-36} \atop {20x+21y=144}} \right.=\left \{ {{-40x+75y=180} \atop {40x+42y=288}} \right.\\\\ 33y=-108\\y=-108:33\\y=-\frac{108}{33}\\\\ 40x+42*(-\frac{108}{33})=288\\\\ 40x-\frac{4536}{33}=288\\\\ 40x=288+\frac{4536}{33}\\\\ 40x=\frac{9504}{33}+\frac{2536}{33}\\\\ 40x=\frac{12040}{33}\\ \\x=\frac{12040}{33}:40\\ x=\frac{12040}{33}*\frac{1}{40}\\\\ x=\frac{301}{33}$

$3)\left \{ {{\frac{6x}{5}+\frac{y}{15}=2.3 } \atop {\frac{x}{10}-\frac{2y}{3}=1.2}} \right.=\left \{ {{18x+y=34.5} \atop {3x-20y=36}} \right. =\left \{ {{y=34.5-18x} \atop {3x-20y=36}} \right. \\\\ 3x-20(34.5-18x)=36\\3x-690+360x=36\\363x=36+690\\363x=726\\x=726:363\\x=2\\\\3*2-20y=36\\6-20y=36\\-20y=36-6\\-20y=30\\y=30:(-20)\\y=-1.5$