Question

resolva estes sistemas pelo metodo da adição.

a)3x-2y=10
5x+2y=22

b)-a+2b=7
a-3b=-9

c)a+3b=5
2a-3b=-8

d)2a-b=-3
6a+b=7

Answer 1

a)

3x - 2y = 10
5x + 2y = 22

3x + 5x - 2y + 2y = 10 + 22
8x = 32
x = 32/8
x = 4

3x - 2y = 10
3.(4) - 2y = 10
12 - 2y = 10
- 2y = 10 - 12
- 2y = -2
y = 2/2
y = 1

S = {4,1}

b) 

- a + 2b = 7
  a - 3b = -9

- a + a + 2b - 3b = 7 - 9
- b = -2
b = 2

a - 3b = -9
a - 3.(2) = -9
a - 6 = -9
a = - 9 + 6
a = - 3

S = {-3,2}

c)

a + 3b = 5
2a - 3b = -8

a + 2a + 3b - 3b = 5 - 8
3a = - 3
a = -3/3
a = - 1

a + 3b = 5
- 1 + 3b = 5
3b = 5 + 1
3b = 6
b = 6/3
b = 2

S = {-1,2}

d)

2a - b = -3
6a + b = 7

2a + 6a - b + b = - 3 + 7
8a = 4
a = 4/8
a = 1/2

2a - b = -3

2.(1/2) - b = -3

1 - b = - 3

- b = - 3 - 1

- b = - 4

b = 4

S = {1/2,4}

Answer 2

a) 8x =10 +22⇒8x=32⇒x=4
3x-2y= 10⇒3.(4) -2y=10⇒12-2y=10⇒-2y=10-12⇒y=1.
S={ 4,1}

b) -b=-2(-1)⇒b=2
-a+2b= 7⇒-a+2.2=7⇒-a=7-4⇒a=3 S={ 3,2}

c) 3 a=-3⇒ a=-1.
a+3b=5⇒ -1+3b=5⇒b=6/3⇒b=2 S={-1,2}

d) 8a=4 ⇒a=1/2.
2 (1/2) -b=-3
1-b=-3⇒b=4 
S={1/2,4}