Question

Escreva os pares de sistemas equivalentes.
A){6x+y=1
-2x+y=-3

B){x-y=2
-2x+y=1

C){-x+2y=6
x-4y=-12

D){1/3x-y=4
-x+1/5y=2

E){2x+y=-1
4x-y=4

Answer 1

a)6x+y=1 (2)
-2x+y=-3 (6)

12x+2y=2
-12x+6y=-18
__________
8y= -16
y= -16/8
y= -2

6x+y=1
6x+(-2)=1
6x-2=1
6x=1+2
6x=3
x=3/6(÷3)
x=1/2

b)x-y=2 (4)
-2x+y=1 (2)

4x-4y=8
-4x+2y=2
________
-2y=10
-y= 10/2
-y=5(-1)
y=-5

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

c)-x+2y=6 (5)
x-4y=-12 (5)

-5x+10y=30
5x-20y=-60
__________
-10y=-30
-y= -30/10
-y=-3 (-1)
y=3

x-4y=-12
x-4(3)=-12
x-12=-12
x=-12+12
x=0

d) 1/3x-y=4
-x+1/5y=2
-----------------
x-3y=4(5)
-5x+y=2
-----------------
5x-15y=20
-5x+y=2
_________
-14y=22
-y=22/14(÷2)
-y=11/7(-1)
y=- 11/7

x-3y=4
x-4(-11/7)=4
x+44/7=4
x=4-44/7 (m.m.c=7)
x=28-44/7
x=- 16/7

e)2x+y=-1 (4)
4x-y=4 (4)

8x+4y=-4
16x-4y=16
________
24x=12
x=12/24(÷12)
x=1/2

4x-y=4
4(1/2)-y=4
4/2-y=4
2-y=4
-y=4/2
-y=2(-1)
y=- 2