Question

2) Resolva os sistemas pelo método de adição

a) x+y= 9
2x-y= 3

b) 6x+3y= 27
2x-y= 3

c) 5x-4y= 4
5x+4y= 36​

Answer 1

Resposta:

a) $(4,~5)$

b) $(3,~3)$

c) $(4,~4)$

Explicação passo-a-passo:

a)

$~x + y = 9\\\underline{2x - y = 3~~}\\3x~~~~~=12~\Rightarrow x = \frac{12}{3} \Rightarrow x = 4\\\\x + y = 9\\(4) + y = 9\\y = 9 - 4\\y = 5$

b)

$6x + 3y = 27~~\Rightarrow 6x+3y = 27\\2x-y =3^{~(3)}~\Rightarrow \underline{6x-3y=~9~}\\~~~~~~~~~~~~~~~~~~~~~~~~~12x~~~~~=36~\Rightarrow x = \frac{36}{12} \Rightarrow x = 3\\\\6x + 3y = 27\\6(3) + 3y = 27\\18 + 3y = 27\\3y = 27-18\\3y = 9\\y = \frac{9}{3}\\y = 3$

c)

$5x -4y = 4\\\underline{5x+4y=36~}\\10x~~~~~= 40~~\Rightarrow x = \frac{40}{10} \Rightarrow x = 4\\\\5x + 4y = 36\\5(4) + 4y = 36\\20 + 4y = 36\\4y = 36-20\\4y = 16\\y = \frac{16}{4}\\y = 4$