Question

What is the solution to the following system?

3x + 10y -12z = 40
x - 5y = 0
x- 4z = 0

--------------------------------------------------------------------

A.) (8, 40, 32)

B.) (10, 2, 3)

C.) (20, 4, 5)

D.) (40, 8, 10)

Answer 1

Answer: C.) (20, 4, 5)

Explanation:

The given system is

`3x + 10y-12z = 40.....................(1)\\x-5y =0..........................(2)\\x- 4z=0............................(3)`

From (2), we have

`x=5y\\\Rightarrow\ y=(x)/(5)`

From (3)

`x=4z\\\Rightarrow\ z=(x)/(4)`

Substitute the values of y and z in equation (1), we get

`3x+10((x)/(5))-12((x)/(4))=40\\\\\Rightarrow\ 3x+2x-3x=40\\\\\Rightarrow\ 20x=40\\\\\Rightarrow\ x=5`

Then
`y=(20)/(5)=4`

and
`z=(20)/(4)=5`

Hence, the solution of the given system is (20,4,5)

Answer 2

Selection C is appropritate.