Question

Resolva os sistemas abaixo pelo método de substituição:
a) x+y= 18
x-y=2

b)3x-4y=0
2x-y=5

Answer 1

a)

x+y=18
x-y=2

x=18-y
x-y=2

x=18-y
(18-y)-y=2

x=18-y
-2y+18=2

x=18-y
-2y=2-18

x=18-y
-2y=-16

x=18-y
y=-16/-2

x=18-y
y=8

x=18-8
y=8

x=10
y=8

b)

3x-4y=0
2x-y=5

2x-y=5
3x-4y=0

2x=5+y
3x-4y=0

x=(5/2)+(y/2)
3x-4y=0

x=(5/2)+(y/2)
3(5/2)+(y/2)-4y=0

x=(5/2)+(y/2)
3(5/2)+3(y/2)-4y=0

x=(5/2)+(y/2)(3/1)(5/2)+(3/1)(5/2)-4y=0

x=(5/2)+(y/2)
(3y/2)+(15/2)-4y=0

x=(5/2)+(y/2)
(3y/2)+(15/2)+(-4y/1)(2/2)=0

x=(5/2)+(y/2)
(3y/2)+(15/2)+((-4y×2)/2)=0

x=(5/2)+(y/2)
((3y-4y×2)/2)+(15/2)=0

x=(5/2)+(y/2)
((y×3-4y×2)/2)+(15/2)=0

x=(5/2)+(y/2)
((y×3-y(-4×2))/2)+(15/2)=0

x=(5/2)+(y/2)
((y×(3-4×2))/2)+(15/2)=0

x=(5/2)+(y/2)
((y×(3-8))/2)+(15/2)=0

x=(5/2)+(y/2)
((y×(-5))/2)+(15/2)=0

x=(5/2)+(y/2)
(-(y×5)/2)+(15/2)=0

x=(5/2)+(y/2)
-(5y/2)+(15/2)=0

x=(5/2)+(y/2)
-(5y/2)=-(15/2)

x=(5/2)+(y/2)
-5y=-(15/2)×2

x=(5/2)+(y/2)
-5y=-(30/2)

x=(5/2)+(y/2)
-5y=-15

x=(5/2)+(y/2)
y=(-15)/(-5)

x=(5/2)+(y/2)
y=3

x=(5/2)+(3/2)
y=3

x=(5+3)/2
y=3

x=8/2
y=3

x=4
y=3

A letra b foi meio complicado, mas espero que entenda, se houver alguma duvida, me avise

Bons estudos!!