Question

Aplicando o método da substituição, resolva os seguintes sistemas:
$A)\left \{ {{x-y=5} \atop {x+3y=9}} \right.$

$B)\left \{ {{3x-2y=6} \atop {x-3y=2}} \right.$

$C)\left \{ {{x+y=4} \atop {2x+y=7}} \right.$

Answer 1

a) $\left \{ {{x-y=5} \atop {x+3y=9}} \right.$

x= 5+y

x+3y=9

5+y+3y=9

5+4y=9

4y=9- 5

4y=4

y=4/4

y=1

x=5+y-->x= 5+1--> x=6

b) $\left \{ {{3x-2y=6} \atop {x-3y=2}} \right.$

x=2+3y

3x-2y=6

3(2+3y)-2y=6

*distributiva*

6+9y-2y=6

6+7y=6

7y=6-6

7y=0

y=0/7

y=0

x= 2+3y--> x= 2+3.0--> x=2+0-->x=2

c)$\left \{ {x+y=4} \atop {2x+y=7}} \right.$

x=4-y

2x+y=7

2(4-y)+y=7

8-2y+y=7

8-y=7

-y=7-8

-y=-1 .(-1)

y= 1

x=4-y--> x=4-1--> x=3