Question

Use o método de substituição e resolva o sistema a seguir em IR

$\left \{ { \frac{x}{6} - \frac{y}{3} = \frac{2}{3} } \atop { \frac{x}{6} + {2 y} = \frac{4}{3} } \right.$

Answer 1

$\left \{ {{ \frac{x}{6} - \frac{y}{3} = \frac{2}{3} } \atop { \frac{x}{6} - 2y = \frac{4}{3}}} \right. \\ \\ \frac{x}{6} - 2y = \frac{4}{3} \\ \frac{x-12y}{6} = \frac{4}{3} \\3x-36y=24 \\ \\ \frac{x}{6} - \frac{y}{3} = \frac{2}{3} \\ \\ \frac{\frac{24+36y}{3} }{6} - \frac{y}{3} = \frac{2}{3} \\ \\\frac{24+36y}{3} . \frac{1}{6} - \frac{y}{3} = \frac{2}{3} \\ \\ \frac{24+36y}{18} - \frac{y}{3} = \frac{2}{3}$
$\\ \frac{24}{18} + \frac{36y}{18} - \frac{y}{3} = \frac{2}{3} \\ \\ \frac{24+36-6y}{18} =\frac{2}{3} \\ \\ \frac{60-6y}{18} =\frac{2}{3} \\ \\180-18y=36 \\ \\-18y=36-180 \\ \\y= \frac{-144}{-18} = 8$


$x= \frac{24+36y}{3} \\ \\x=\frac{24+36.8}{3} \\ \\x=\frac{312}{3} = 104$