Question

1• Utilizando o método da substituição, determine a solução de cada um dos seguintes sistemas de equações do 1° grau nas incógnitas x e y:

helpp e pra entregar hoje! (com o calculo!!)​

Answer 1

$\Large\boxed{\begin{array}{l}\tt a)\\\begin{cases}\sf x+y=22\\\sf x-y=8\end{cases}\\\begin{cases}\sf y=22-x\\\sf x-y=8\end{cases}\\\sf x-(22-x)=8\\\sf x-22+x=8\\\sf 2x=8+22\\\sf 2x=30\\\sf x=\dfrac{30}{2}\\\\\sf x=15\\\sf y=22-x\\\sf y=22-15\\\sf y=7\\\sf S=\{15,7\}\blue{\checkmark}\end{array}}$

$\Large\boxed{\begin{array}{l}\tt b)\\\begin{cases}\sf 2x+y=26\\\sf x-y=4\end{cases}\\\\\begin{cases}\sf 2x+y=26\\\sf y=x-4\end{cases}\\\sf 2x+x-4=26\\\sf 3x=4+26\\\sf 3x=30\\\sf x=\dfrac{30}{3}\\\\\sf x=10\\\sf y=x-4\\\sf y=10-4\\\sf y=6\\\sf S=\{10,6\}\blue{\checkmark}\end{array}}$

$\Large\boxed{\begin{array}{l}\tt c)\\\begin{cases}\sf3x+y=-5\\\sf5x-2y=-1\end{cases}\\\\\begin{cases}\sf y=-3x-5\\\sf 5x-2y=-1\end{cases}\\\sf 5x-2\cdot(-3x-5)=-1\\\sf 5x+6x+10=-1\\\sf 11x=-1-10\\\sf 11x=-11\\\sf x=-\dfrac{11}{11}\\\\\sf x=-1\\\sf y=-3x-5\\\sf y=-3\cdot(-1)-5\\\sf y=3-5\\\sf y=-2\\\sf S=\{-1,-2\}\blue{\checkmark}\end{array}}$

$\Large\boxed{\begin{array}{l}\tt d)\\\begin{cases}\sf x+2y=-4\\\sf3x-2y=20\end{cases}\\\\\begin{cases}\sf x=-2y-4\\\sf 3x-2y=20\end{cases}\\\sf 3\cdot(-2y-4)-2y=20\\\sf -6y-12-2y=20\\\sf 6y+2y=-12-20\\\sf 8y=-32\\\sf y=-\dfrac{32}{8}\\\\\sf y=-4\\\sf x=-2y-4\\\sf x=-2\cdot(-4)-4\\\sf x=8-4\\\sf x=4\\\sf S=\{4,-4\}\blue{\checkmark}\end{array}}$

Answer 2

Resposta:

a)

{x + y = 20 ---> x = 20 - y

{x - y = 8

Substituindo "x":

x - y = 8

20 - y - y = 8

-y - y = 8 - 20

-2y = -12

y = -12/(-2)

y = 6

Substituindo "y":

x = 20 - y

x = 20 - 6

x = 14

b)

{3x - y = 18

{x + y = 10  ---> x = 10 - y

Substituindo "x":

3x - y = 18

3.(10 - y) - y = 18

30 - 3y - y = 18

-3y - y = 18 - 30

-4y = -12

y = -12/(-4)

y = 3

Substituindo "y":

x = 10 - y

x = 10 - 3

x = 7

c)

{2x + y = -3

{x - 3y = -26 ---> x = -26 + 3y

Substituindo "x":

2x + y = -3

2.(-26 + 3y) + y = -3

-52 + 6y + y = -3

6y + y = -3 + 52

7y = 49

y = 49/7

y = 7

Substituindo "y":

x = -26 + 3y

x = -26 + 3.(7)

x = -26 + 21

x = -5

d)

{x + 5y = -24 ---> x = -24 - 5y

{3x - 2y = -4

Substituindo "x":

3x - 2y = -4

3.(-24 - 5y) - 2y = -4

-72 - 15y - 2y = -4

-15y - 2y = -4 + 72

-17y = 68

y = 68/(-17)

y = -4

Substituindo "y":

x = -24 - 5y

x = -24 - 5.(-4)

x = -24 + 20

x = -4

Explicação passo a passo: