2x + 3y + z = -3
x + 4y -3z = -23
3x - y +2x = 14


i've tried to solve it numerous times and keep coming up with decimals / fractions ? just want to make sure i'm not missing something or solving wrong

thanks in advance

first step is to take one of the variables from one of the equations and plug into the other two, so for starters

z = -3 - 2x - 3y

which creates the following two equations with 2 variables:

x + 4y - 3*(-3-2x-3y) = -23 and
3x - y + 2*(-3-2x-3y) = 14

now to simplify

x + 4y + 9 + 6x +9y = 7x +13y + 9 =-23 -> 7x+13y=-32
3x - y - 6 - 4x - 6y = -x - 7y- 6 = 14 -> x+7y=-20

now from the second x = -7y -20 which can be plugged into the other equation

7*(-7y-20)+13y=-32 -> -49y-20+13y=-32 -> -36y=-12 -> y=1/3

now you can plug this into the previous equation etc ... so, yes there are fractions

use substitution/elimination. if you need to double check your answer, simply plug in your [x, y, z] and see if they work. nothing wrong with fractions.

if you have a graphing utility, input your values into a matrix and find reduced row echelon form (rref)