2x+4y+2z = - 8

5y-2z = 0

4z = - 20

The given solution for the system is x = 5, y = - 2 and z = - 5

Step-by-step explanation:

Here, the given set of equations are:

2 x + 4 y + 2 z = - 8

5 y - 2 z = 0

4 z = - 20

Now, simplifying each question one by one, we get:

Simplifying third equation for the value of z:

4 z = - 20 ⇒ z = - 20 / 4 = - 5

or, z = - 5

Simplifying second equation for the value of y:

Substitute the value of z = - 5 in (2), we get

5 y - 2 z = 0 ⇒ 5 y - 2 (-5) = 0

or, 5 y + 10 = 0

or, 5 y = - 10

or, y = - 10/5 = - 2

⇒ y = - 2

Simplifying first equation for the value of x:

Substitute the value of z = - 5 and y = - 2 in (1), we get

2 x + 4 y + 2 z = - 8 ⇒ 2 x + 4 (-2) + 2 (-5) = - 8

or, 2 x - 8 - 10 = - 8

or, 2 x = 10

x = 10 / 2 = 5, or x = 5

Hence, the given solution for the system is x = 5, y = - 2 and z = - 5