Question

e) {3x/2 + y/3 = 6
{x + y = 11

f) {2x + y = 5
{2x - y = -3

Answer 1

Resposta

$a) S = \left\{2,9\right\}$

$b) S=\left\{\frac{1}{2},4\right\}$

Sistemas de Equações de 1º Grau

Método da Substituição

$e) \left \{ {{\frac{3x}{2}+\frac{y}{3} =6} \atop {x+y=11}} \right.$

$x+y=11 \therefore x= 11-y$

$\frac{3(11-y)}{2}+\frac{y}{3}=6$

$mmc(2,3)=6$

$\frac{(6:2).3(11-y)}{6}+\frac{(6:3).y}{8}=\frac{(6:1).6}{6}$

$\frac{3.3(11-y)}{6}+\frac{2y}{6}=\frac{36}{6}$

$\frac{9(11-y)}{6}+\frac{2y}{6}=$ $\frac{36}{6}$

$\frac{99-9y}{6}+\frac{2y}{6}=\frac{36}{6}$  

Ignorando os denominadores:

$99-9y+2y=36$

$-7y = 36-99$

$-7y =-63$

$y = \frac{-63}{7}$

$y= 9$

Calculando x:

$x + y = 11 \therefore x = 11 - y \therefore x= 11-9 \therefore x = 2$

$S = \left\{2,9\right\}$

Método da Adição:

$f) \left \{ {{2x+y=5} \atop {2x-y=-3}} \right.$

$2x+2x + y - y =5 - 3$

$4x =2$

$x=\frac{2}{4}\thereforex = \frac{1}{2}$ ⇒ simplificado por 2

$2x + y = 5\therefore2.\frac{1}{2}+y = 5\therefore1+y = 5\thereforey=5-1\thereforey=4$

$S=\left\{\frac{1}{2},4\right\}$

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