Answer: C.) (20, 4, 5)
Step-by-step explanation:
The given system is
[tex]3x + 10y-12z = 40.....................(1)\\x-5y =0..........................(2)\\x- 4z=0............................(3)[/tex]
From (2), we have
[tex]x=5y\\\Rightarrow\ y=\frac{x}{5}[/tex]
From (3)
[tex]x=4z\\\Rightarrow\ z=\frac{x}{4}[/tex]
Substitute the values of y and z in equation (1), we get
[tex]3x+10(\frac{x}{5})-12(\frac{x}{4})=40\\\\\Rightarrow\ 3x+2x-3x=40\\\\\Rightarrow\ 20x=40\\\\\Rightarrow\ x=5[/tex]
Then [tex]y=\frac{20}{5}=4[/tex]
and [tex]z=\frac{20}{4}=5[/tex]
Hence, the solution of the given system is (20,4,5)
