Question

3x + 0,5y + Z = 14,45

2x + 1y + 2z = 12,90
3x + 3y + 3z = 23,10


Não consigo resolver, alguém me ajuda? é um trabalho da escola.

Answer 1

Answer: x = 4

y = 2,5

z = 1,2

Explanation:

Step 1: Naming the equations

(Eq. 1) : 3x + 0,5y + z = 14,45

(Eq. 2) : 2x + 1y + 2z = 12,90

(Eq. 3) : 3x + 3y + 3z = 23,10

Step 2: Divide (Eq. 3) by 3

`((1)/(3))*(3x + 3y + 3z) = ((1)/(3))*(23,10)`

`x + y + z = 7,7`

This equation is named: (Eq. 4)

Step 3: Multiply (Eq. 4) by -2

(Eq. 4) * (-2): (-2)( x + y + z) = (-2)(7,7)

-2x - 2y - 2z = -15,4

This equation is named: (Eq. 5)

Step 4: Subtract (Eq. 5) from (Eq. 2)

(Eq. 2) - (Eq. 5): 2x + y + 2z = 12,90

- 2x - 2y - 2z = -15,4

- y = -2,5

Then: y = 2,5

Step 5: Subtract (Eq. 3) from (Eq. 1)

(Eq. 1) - (Eq. 3) : 3x + 0,5y + z = 14,45

- 3x - 3y - 3z = -23,1

-2,5y - 2z = -8,65

2,5y + 2z = 8,65

This equation is named: (Eq. 7)

Step 6: Replace the value of y [y = 2,5] in (Eq. 7)

2,5 (2,5) + 2z = 8,65

6,25 + 2z = 8,65

2z = 8,65 - 6,25

2z = 2,4

z = 1,2

Then: z = 1,2

Step 8: Replacing values of y and z [y = 2,5 ; z = 1,2] in (Eq. 3)

3x + 3(2,5) + 3(1,2) = 23,10

3x + 7,5 + 3,6 = 23,10

3x + 11,1 = 23,10

3x = 23,10 - 11,1

3x = 12

x = 4

Then: x = 4

Therefore, the solution is: x = 4

y = 2,5

z = 1,2

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