Question

Resolva os sistemas do 1°grau!

a) x + y = 11
x - y = 3

b) x + 6y = 40
-x + 3y = 5

c) x + y = 6
2x - y = 4

Answer 1

a) $\begin{bmatrix}x+y=11\\ \\ x-y=3\end{bmatrix}\\  \\ x+y=11\\ x+y-y=11-y1-y\\ x=11-y\\ \begin{bmatrix}11-y-y=3\end{bmatrix}\\ 11-y-y=3\\ 11-2y=3\\ 11-2y-11=3-11\\ -2y=-8\\ \frac{-2y}{-2}=\frac{-8}{-2}\\ y=4\\ x=11-4\\ x=7\\ y=4,\:x=7$

b) $\begin{bmatrix}x+6y=40\\ -x+3y=5\end{bmatrix}\\  \\ x+6y=40\\ x+6y-6y=40-6y\\ x=40-6y\\ \begin{bmatrix}-\left(40-6y\right)+3y=5\end{bmatrix}\\ x=40-6\cdot \:5\\ 40-6\cdot \:5\\ =40-30\\ =10\\ x=10\\ y=5,\:x=10$

c) $\begin{bmatrix}x+y=62\\ x-y=4\end{bmatrix}\\  \\ x+y=62\\ x+y-y=62-y\\ x=62-y\\ \begin{bmatrix}62-y-y=4\end{bmatrix}\\ 62-2y=4\\ 62-2y-62=4-62\\-2y=-58 \\ y=29\\ x=62-29\\ =33\\ x=33\\ y=29,\:x=33$