resolva as seguintes sistemas de equação do 1° grau com duas incógnitas :
a) x + y = 10
y = x
b) x - y = 4
x = 3y
c) 2x + 3y = 15
x = y
d) 4x - 3y = 16
y = x - 1
e) x + 2y = 1
y = 6 x
f) y = 2x - 1
y = 4x - 9
g) y = x
y = 2x
h) y = 1 - 2x
y = 3x
i) x = 4 - y
x = y + 6
j) x = 7 - y
x = - 7 + y
k) x + y = 10
x = 7 - y
l) y = 4x - 3
2x - 3y = 5
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Respostas
Resposta:Segue as contas abaixo na explicação
Explicação passo-a-passo:Método de Adição
a) x + y = 10 b) x - y = 4
y = x x = 3y
x+y=10 x-y=4
y-x=0 (-1) x-3y=0 x-y=4
x+y=10 x+y=10 x-y=4 x-2=4
-x+y=0 x+5=10 -x+3y=0 x-2+2=4+2
2y=10 x+5-5=10-5 2y=4 x=6
y=10/2 x=5 y=4/2
y=5 y=2
S(5,5) S(6,2)
c) 2x + 3y = 15 d) 4x - 3y = 16
x = y y = x - 1
2x+3y=15 4x-3y=16 4x-3y=16
(3) x-y=0 y-x=-1 4.13-3y=16
2x+3y=15 2x+3y=15 4x-3y=16 52-3y=16
3x-3y=0 2.3+3y=15 (3) -x+y=-1 52-52-3y=16-52
5x=15 6+3y=15 4x-3y=16 -3y=-36(-1)
x=15/5 6-6+3y=15-6 -3x+3y=-3 3y=36
x=3 3y=9 x=13 y=36/3
y=9/3 y=3
y=3 S(13,3)
e) x + 2y = 1 f) y = 2x - 1
y = 6 x y = 4x - 9
x+2y=1 (-2) y-2x=-1 y-4x=-9
y-6x=0 y-4x=-9 7-4x=-9
(6) x+2y=1 x+2y=1 -2y+4x=2 7-7-4x=-9-7
-6x+y=0 x+2.6/13=1 y-4x=-9 -4x=-16(-1)
6x+12y=6 x+12/13=1 -y=-7(-1) 4x=16
-6x+y=0 13x/13+12/13=13/13 y=7 x=16/4
13y=6 13x+12=13 x=4
y=6/13 13x+12-12=13-12 S(4,7)
13x=1
x=1/13
S(1/13,6/13)
g) y = x h) y = 1 - 2x
y = 2x y = 3x
(-1) y-x=0 y-x=0 y+2x=1
y-2x=0 y-0=0 (-1) y-3x=0 y+2x=1
-y+x=0 y=0 y+2x=1 y+2.1/5=1
y-2x=0 -y+3x=0 y+2/5=1
-x=0(1) 5x=1 5y/5+2/5=5/5
x=0 x=1/5 5y+2=5
S(0,0) 5y+2-2=5-2
5y=3
y=3/5
S(1/5,3/5)
i) x = 4 - y j) x = 7 - y
x = y + 6 x = - 7 + y
x+y=4 x+y=4 x+y=7 x+y=7
x-y=6 5+y=4 x-y=-7 0+y=7
2x=10 5-5+y=4-5 2x=0 y=7
x=10/2 y=-1 x=0/2
x=5 x=0
S(5,-1) S(0,7)
k) x + y = 10 l) y = 4x - 3
x = 7 - y 2x - 3y = 5
x+y=10 y-4x=-3
(-1) x+y=7 2x-3y=5
x+y=10 (3)-4x+y=-3 -4x+y=-3
-x-y=-7 2x-3y=5 -4.2/5+y=-3
0x+0y=3 -12x+3y=-9 -8/5+y=-3
É impossível(não há soluções) 2x-3y=5 -8/5+5y/5=-15/5
-10x=-4(-1) -8+5y=-15
10x=4 -8+8+5y=-15+8
x=4/10:2/2 5y=-7
x=2/5 y=-7/5
S(2/5,-7/5)