Question

Resolva Os sistemas a seguir, pelo método da adição:
a) x+4y=-3
-3x-y=-24

b) x+y=-1
x+5y=3

c)2x+y=4
x-2y=-3

d) 3x-y=5
2x+3y=18

e) x-5y=6
2x+y=1

Answer 1

a) x+4y=-3
x=-3-4y

-3x-y=-24
-3.(-3-4y)-y=-24
9-4y-y=-24
-5y=-24-9
-5y=-33
y=(-33) / (-5)
y=33/5

x=-3-4y
x=-3-4.(33/5)
x=-3-(132/5)
x=-147/5

b) x+y=-1
y=-1-x

x+5y=3
x+5.(-1-x)=3
x-5-5x=3
-4x=3+5
x=8/(-4)
x=-2

y=-1-(-2)
y= 1

c)2x+y=4
y=4-2x

x-2y=-3
x-2.(4-2x)=-3
x-8+4x=-3
3x=-3+8
x=5/3

y=4-2.(5/3)
y=4-(10/3)
y=-78/3
y=-26

d) 3x-y=5
y=5-3x

2x+3y=18
2x+3.(5-3x)=18
2x+15-9x=18
2x-9x=18-15
-7x=3
x=3/(-7)
x=-3/7

y=5-3.(-3/7)
y=5+9/7
y=44/7

e) x-5y=6
x=6+5y

2x+y=1
2.(6+5y)+y=1
12+10y+y=1
10y+y=1-12
11y=-11
y=-11/11
y=-1

x=6+5.(-1)
x=6-5
x=1