Question

classifique e resolva o sistema {x-3y=2 {x+2y=1​

Answer 1

Método de eliminação

$\begin{bmatrix}x-3y=2\\ x+2y=1\end{bmatrix}\\ \\  x-3y=2\\ x-3y+3y=2+3y\\ x=2+3y\\ \begin{bmatrix}2+3y+2y=1\end{bmatrix}\\ 2+3y+2y=1\\ 2+5y=1\\ 2+5y-2=1-2\\ 5y=-1\\ \frac{5y}{5}=\frac{-1}{5}\\ y=-\frac{1}{5}\\  \\ x=2+3\left(-\frac{1}{5}\right)\\ 2+3\left(-\frac{1}{5}\right)=\frac{7}{5}\\ 2+3\left(-\frac{1}{5}\right)\\ =2-3\cdot \frac{1}{5}\\ 3\cdot \frac{1}{5}=\frac{3}{5}\\ 3\cdot \frac{1}{5}\\ =\frac{1\cdot \:3}{5}\\ =\frac{3}{5}\\ =2-\frac{3}{5}\\ =\frac{2\cdot \:5}{5}-\frac{3}{5}$

$=\frac{2\cdot \:5-3}{5}\\ 2\cdot \:5-3=7\\ 2\cdot \:5-3\\ =10-3\\ =7\\ =\frac{7}{5}\\ x=\frac{7}{5}\\ y=-\frac{1}{5},\:x=\frac{7}{5}$