Question

resolva os sistemas de equação de 1 grau

A) x+ y=6
x - y=2

B) 2x+y=18
x-y=8

C) 3x+2y=16
2x-y=14

D) x+2y=12
x-y=2

Answer 1

Milena, 
A solução do sistema não é nada complicado
Ajudo com as duas primeiras

A)
          x + y = 6      (1)
          x - y =2      (2)
            (1) + (2)
                         2x = 8
                           x = 8/2
                                                 x = 4
            x em (2)
                        4 - y = 2
                         4 - 2 = y
                                                 y = 2               SOLUÇÃO SISTEMA
                                                                                     x = 4
                                                                                     y = 2
B)
          2x + y = 18     (1)
           x - y = 8         (2)
       Igual anterior
           (1) + (2)
                 3x = 24
                                     x = 26/3        
         x em (2)
                 26/3 - y = 8
                 26/3 - 8 = y
                 26/3 - 24/3 = y         y = 2/3

 

Answer 2

$C)~~\begin{cases}3x+2y=16\\ 2x-y=14\end{cases}\\\\\\ 2x-y=14\to~~ -y=-2x+14~(-1)\to~~ y=2x-14\\\\\\3x+2y=16\to~~ 3x+2(2x-14)=16\to~~ 3x+4x-28=16\to\\ \\ 7+28\to~~ 7x=44\to~~ \boxed{x= \frac{44}{7}}\\\\\\ y=2x-14\to ~~ y=2. \dfrac{44}{7} -14\to ~~ y= \dfrac{88}{7} -14\to \\\\ y= \dfrac{88-98}{7} \to ~~ \boxed{y= - \frac{10}{7} }\\\\\\\\\\ \large\boxed{ \boxed{S=\left\{ \frac{~44}{7} ~; ~-\frac{10}{7} \right\}}}$






$D)~~\begin{cases}x+2y=12\\ x-y=2\end{cases}\\\\\\ x-y=2\to~~ x=y+2\\\\\\ x+2y=12\to~~ y+2+2y=12\to~~ y+2y=12-2\to~~ 3y=10\to \\\\ \boxed{y= \frac{10}{3} }\\\\\\ x=y+2\to~~ x=\dfrac{10}{3} +2\to~~ x=\dfrac{10+6}{3} \to~~ \boxed{x=\frac{16}{3} }\\\\\\\\ \large\boxed{ \boxed{S=\left\{ \frac{16}{3} ~; ~\frac{10}{3} \right\}}}$