Question

Escalone e resolva os sistemas.
a) {x+y=5
{2x-y=1
b) {2x+2y=4
{x-3y=6
c) {4x-2y=34
{x+6y=2
d) {x+y=-4
{3x-2y=3​

Answer 1

Resposta:

a)

x + y = 5

(=) y = 5 - x ...(i)

2x - y = 4

2x - 4 = y ...(ii)

From equacão i) e ii)

2x - 4 = 5 - x

(=) 2x + x = 5 + 4

(=) 3x = 9

(=) x = 9÷3

(=) x = 3

equacão i)

y = 5 - x

(=) y = 5 - 3

(=) y = 2

s= (x = 3, y = 2)

b) 2x + 2y = 4

(=) 2 (x + y) = 4

(=) (x + y) = 4÷2

(=) x + y = 2

(=) x = 2 - y ...(i)

x - 3y = 6

(=) x = 6 + 3y ...(ii)

From equacão i) e ii)

6 + 3y = 2 - y

(=) 3y + y = 2 - 6

(=) 4y = -4

(=) y = - 4 ÷ 4

(=) y = -1

Em equação i)

x = 2 - y

(=) x = 2 - (-1)

(=) x = 2 + 1

(=) x = 3

s =(x = 3 , y= -1

c)

4x -2y = 34

(=) 2 ( 2x - y) = 34

(=) 2x - y = 34 ÷ 2

(=) 2x - y = 17

(=) 2x - 17 = y .... (i)

x + 6y = 2

(=) x + 6 ( 2x - 17 ) = 2

(=) x + 12x - 102 = 2

(=) 13x = 102 + 2

(=) 13 x = 104

(=) x = 104 ÷ 13

(=) x = 8

y= 2x - 17

(=) y = 2×8 -17

(=) y = -1

s = (x= 8, y = -1

d)

x + y = -4

x = -4 -y ...(i)

3x - 2y = 3

(=) 3(-4 -y) - 2y = 3

(=) -12 - 3y - 2y = 3

(=) - 5y = 15

(=) y = 15 ÷ (-5)

(=) y= -3

x= -4 -(-3)

(=) x = -1

s = ( x = -1 , y= -3