Question

resolva os sistemas pelo metodo da substituição:
a)x+y=4
3x+y=28


b)4x+y=0
x+5y=-19


c)-2x-3y=-9
x+4y=12


d)-6x+2y=8
9x-y=8



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Answer 1

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

3x + y = 28
3(4-y) + y = 28
12 - 3y + y = 28
12 - 2y = 28
-2y = 18-12
-2y = 6
y = 6/-2
y = -3
x = 4-y
x = 4-(-3)
x = 4+3
x = 7


b)
4x + y = 0
4x = -y
x = -y/4

x + 5y = -19
-y/4 + 5y = -19
-y + 4.(5y) = -19.(4)
-y + 20y = -76
19y = -76
y = -76/19
y = -4
x = -y/4
x = -(-4)/4
x = 4/4
x = 1


c)
-2x-3y = -9
-2x = -9+3y
x = -9+3y/-2

x + 4y = 12
(-9 + 3y)/-2 + 4y = 12
(9 -3y)/2 + 4y = 12
9 -3y + 2.(4y) = 12.2
9 - 3y + 8y = 24
9 + 5y = 24
5y = 24-9
5y = 15
y = 15/5
y = 3
x = -9 + 3y/-2
x = -9 + 3(3)/-2
x = -9+9/-2
x = 0/-2
x = 0


d)
-6x + 2y = 8
-6x = 8-2y
x = 8-2y/-6

9x -y = 8
9(8-2y)/-6 -y = 8
(72 -18y)/-6 -y = 8
-(72)+18y)/6 -y = 8
-72 + 18y -6(y) = 8.6
-72 + 18y - 6y = 48
-72 + 12y = 48
12y = 48+72
12y = 120
y = 120/12
y = 10
x = 8-2y/-6
x = 8-2(10)/-6
x = 8-20/-6
x = -12/-6
x = 2