Question

Determine o conjunto solução

{3(x+2)+2(y-1)=6
{5(x+3)+3(y+5)=8

Answer 1

Utilizando o método da substituição

$\begin{bmatrix}3\left(x+2\right)+2\left(y-1\right)=0\\ 5\left(x+3\right)+3\left(y+5\right)=8\end{bmatrix}$

$\mathrm{Isolar}\:x\:\mathrm{de}\:3\left(x+2\right)+2\left(y-1\right)=0:\quad x=-\frac{2\left(y-1\right)}{3}-2$

$3\left(x+2\right)+2\left(y-1\right)=0$

$\mathrm{Subtrair\:}2\left(y-1\right)\mathrm{\:de\:ambos\:os\:lados}$

$3\left(x+2\right)+2\left(y-1\right)-2\left(y-1\right)=0-2\left(y-1\right)$

$\mathrm{Simplificar}$

$3\left(x+2\right)=-2\left(y-1\right)$

$\mathrm{Dividir\:ambos\:os\:lados\:por\:}3$

$\frac{3\left(x+2\right)}{3}=\frac{-2\left(y-1\right)}{3}$

$\mathrm{Simplificar}$

$x+2=-\frac{2\left(y-1\right)}{3}$

$\mathrm{Subtrair\:}2\mathrm{\:de\:ambos\:os\:lados}$

$x+2-2=-\frac{2\left(y-1\right)}{3}-2$

$\mathrm{Simplificar}$

$x=-\frac{2\left(y-1\right)}{3}-2$

$\mathrm{Substituir\:}x=-\frac{2\left(y-1\right)}{3}-2$

$\begin{bmatrix}5\left(-\frac{2\left(y-1\right)}{3}-2+3\right)+3\left(y+5\right)=8\end{bmatrix}$

$\mathrm{Isolar}\:y\:\mathrm{de}\:5\left(-\frac{2\left(y-1\right)}{3}-2+3\right)+3\left(y+5\right)=8:\quad y=46$

$\mathrm{Para\:}x=-\frac{2\left(y-1\right)}{3}-2$

$\mathrm{Substituir\:}y=46$

$x=-\frac{2\left(46-1\right)}{3}-2$

$-\frac{2\left(46-1\right)}{3}-2=-32$

$x=-32$

O conjunto solução do sistema de equaçoes acima é:

$y=46,\:x=-32$

Bons estudos!!