What is the solution to the system of equations?

2x+y−z=−3

5x−2y+2z=24

3x−z=5

Guest Aug 29, 2018

#1**+2 **

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)

CPhill Aug 29, 2018