What is the solution to the system of equations?

2x+y−z =−3

5x−2y+2z = 24

3x−z = 5    (1)

Using the last equation    z = 3x  - 5

Using (1) and the first equation we get :

2x + y - (3x - 5)  =  -3

2x + y - 3x + 5  = -3

-x + y + 5  = -3

y  = x - 8   (2)

Sub  (1)  and (2) into  the second equation and we have

5x - 2(x - 8 ) + 2(3x - 5)  = 24

5x  - 2x + 16 + 6x - 10  = 24

9x + 6  = 24  subtract 6 from each side

9x  =18  divide both sids by 9

x  = 2

And using (2)... y  = 2 - 8   =  -6

And z = 3(2) - 5  = 6  - 5   = 1

So   (x, y, z)  = ( 2, -6, 1)