Question

What is the solution to the following system?

Answer 1

The correct answer is option 3. (20, 4, 5)

Explanation:

To solve this problem we use the substitution method.

`3x + 10y -12z = 40` (i)

`x-5y = 0` (ii)

`x - 4z = 0` (iii)

We start by clearing x in (iii) and clearing y in (ii).

`x = 4z` (iii)

`y = (1)/(5)x` (ii)

Now we substitute (iii) in (ii)

`y = (4)/(5)z` (iv)

Now we substitute (iii) and (iv) into (i) and clear z.

`12z + (40)/(5)z -12z = 40` (v)

`8z = 40`

`z = (40)/(8)`

`z = 5`

If
`z = 5` (v)

We substitute (v) in (iii) and then substitute (v) in (iv)

`x = 20\\y = 4\\z = 5`

The correct answer is option 3.