I am trying to figure out how to solve system of equations in 3 variables and the equations are..2x-y-3z=-1,2x-y+2=-9,x+2y-4z=17
First of all, Alba, the second equation must be 2x-y+z=-9 knowing that all the equations must have three variables. Now, on with the procedure. First, it is preferable to label the three equations in the system.
Notice that equations  and  have the same two first terms. The idea here is to solve both equations for 2x-y.
2x-y-3z=-1 is equivalent to 2x-y=3z - 1.
2x-y+z=-9 is equivalent to 2x-y=-z - 9.
Since the left-hand side of both equivalent equations are equal, the right-hand side of both equations can be equalled so the value of z can be found.
3z - 1 = -z - 9
3z + z = 1 - 9
4z = -8
z = -2
Now the value of z is found we have to find out what are the values of the x and y. We'll consider equations  and . To make this procedure easier, we'll substitute the value of z in both equations.
In  when z = -2, 2x-y+(-2)=-9 or 2x-y=-9+2 or 2x-y=-7, which I will label it .
In  when z = -2, x+2y-4(-2)=17 or x+2y+8=17 or x+2y=17-8 or x+2y=9, which I will label it .
For the next step, I can eliminate any of the two variables in  and . Randomly, I can eliminate x. To eliminate x, multiply  by -2 and add it to .
-5y=-25 or y=5
Having found the values of both y and z, use any of the three equations and substitute the corresponding values of both variables to find the value of x. I will use  for the final step.
So the solution is (-1, 5, -2).