Answer: x = 4
y = 2,5
z = 1,2
Step-by-step 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
[tex](\frac{1}{3})*(3x + 3y + 3z) = (\frac{1}{3})*(23,10)[/tex]
[tex]x + y + z = 7,7[/tex]
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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