Question

Escolha um método de resolução e encontre a soluçao destes sistemas:
A)X+y=22
2x-y=20

B)2x-y=4
X+2y=-3

C) 7x-y= -2
X+5y= -26

Answer 1

Usando o método de substituição..

A)

$\begin{bmatrix}x+y=22\\ 2x-y=20\end{bmatrix}\\\\\begin{bmatrix}2\left(22-y\right)-y=20\end{bmatrix}\\\\\begin{bmatrix}44-3y=20\end{bmatrix}\\\\44-3y=20\\\\44-3y-44=20-44\\\\-3y=-24\\\\\frac{-3y}{-3}=\frac{-24}{-3}\\\\y=8\\\\x=22-8\\\\x=14\\\\x=14,\:y=8$

B)

$\begin{bmatrix}2x-y=4\\ x+2y=-3\end{bmatrix}\\\\\begin{bmatrix}\frac{4+y}{2}+2y=-3\end{bmatrix}\\\\\begin{bmatrix}\frac{4+5y}{2}=-3\end{bmatrix}\\\\\frac{2\left(4+5y\right)}{2}=2\left(-3\right)\\\\4+5y=-6\\\\4+5y-4=-6-4\\\\5y=-10\\\\\frac{5y}{5}=\frac{-10}{5}\\\\y=-2\\\\x=\frac{4-2}{2}\\\\x=1\\\\x=1,\:y=-2$

C)

$\begin{bmatrix}7x-y=-2\\ x+5y=-26\end{bmatrix}\\\\\begin{bmatrix}\frac{-2+y}{7}+5y=-26\end{bmatrix}\\\\\begin{bmatrix}\frac{-2+36y}{7}=-26\end{bmatrix}\\\\\frac{-2+36y}{7}=-26\\\\\frac{7\left(-2+36y\right)}{7}=7\left(-26\right)\\\\-2+36y=-182\\\\-2+36y+2=-182+2\\\\\frac{36y}{36}=\frac{-180}{36}\\\\y=-5$

$x=\frac{-2-5}{7}\\\\\frac{-2-5}{7}\\\\=\frac{-7}{7}\\\\=-\frac{7}{7}\\\\=-1$

$x=-1$

$x=-1,\:y=-5$

Answer 2

Resposta:

a) x+y=22

2x-y=20 isolando temos 3x=42 x= 14, logo 14+y=22 y=22-14 y=8

logo x=14,y=8

b) 2x-y=4

(x+2y=-3) vamos multiplicar por -2 para poder anular com a de cima

fica -2x-4y+6

ficamos então com 2x-y=4 e -2x-4y+6= -5y=10 y=10/-5 y=-2

agora que sabemos o valor de y apenas substituir

2x-(-2)= 4, 2x+2=4 2x=2 x=1

x=1 , y=-2

c) 7x-y= -2

X+5y= -26 , x=-5y-26, -35y-y=180 y=-5

x+5y=-26 x=-1

logo x=-1 e y=-5