Answer:
The correct answer is option 3. (20, 4, 5)
Step-by-step explanation:
To solve this problem we use the substitution method.
[tex]3x + 10y -12z = 40[/tex] (i)
[tex]x-5y = 0[/tex] (ii)
[tex]x - 4z = 0[/tex] (iii)
We start by clearing x in (iii) and clearing y in (ii).
[tex]x = 4z[/tex] (iii)
[tex]y = \frac{1}{5}x[/tex] (ii)
Now we substitute (iii) in (ii)
[tex]y = \frac{4}{5}z[/tex] (iv)
Now we substitute (iii) and (iv) into (i) and clear z.
[tex]12z + \frac{40}{5}z -12z = 40[/tex] (v)
[tex]8z = 40[/tex]
[tex]z = \frac{40}{8}[/tex]
[tex]z = 5[/tex]
If [tex]z = 5[/tex] (v)
We substitute (v) in (iii) and then substitute (v) in (iv)
[tex]x = 20\\y = 4\\z = 5[/tex]
The correct answer is option 3.
