Question

What is the solution to the following system?

Answer 1

Answer:

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

Step-by-step 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)

$y = \frac{1}{5}x$ (ii)

Now we substitute (iii) in (ii)

$y = \frac{4}{5}z$ (iv)

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

$12z + \frac{40}{5}z -12z = 40$ (v)

$8z = 40$

$z = \frac{40}{8}$

$z = 5$

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.