i dont know how to solve this 3 variable system of equations and i keep getting stuck

x+y+z=8

x+4y+6z=24

Guest Sep 15, 2019

#1**+1 **

We have more variables than equations....so.....we will have infinite solutions

Subtracting the first equation from the second we get that 3y + 5z = 16 →

3y = [ 16 - 5z] → y = [ 16 - 5z ] / 3

And using the first equation

x + y + z = 8

x + [ 16 - 5z]/3 + z = 8 multiply through by 3

3x + 16 -5z + 3z = 24

3x - 2z = 8

3x = 8 - 2z

x = [ 8-2z] /3

So....the solutions for {x, y , z } = { [8-2z]/3 , [16-5z]/3 , z }

For example...if z = 0, then x = 8/3 and y = 16/3

So....check that these solutions work :

x + y + z = 8 ???

8/3 + 16/3 + 0 = 8 ???

24/3 = 8 ???

True

And

x + 4y + 6z = 24 ???

(8/3) + 4 [16/3] + 0 = 24??

8/3 + 64/3 = 24 ???

72/3 = 24 ???

True

So..... * one* possible solution is { x, y , z} = (8/3, 16/3 , 0 }

CPhill Sep 15, 2019