You can put this solution on YOUR website!
If you know matrices, you can use that. But I suspect you are not there yet.
So, you might try substitution.
I would start with equation 3. Use it to find y in terms of x
You can then substitute that value for y into both equations 1 and 2.
Simplify this to get an equation with just x and z in it
Use it to find x in terms of z
Simplify this one too and get an equation with just x and z.
Substitute the z value in this last equation with the "z in terms of x" from the earlier equation.
You now have one equation with only x and constants in it.
Solve for x.
Niw use this value of x and the equation with z in terms of x to find z.
Then use x and z in any of the equations to solve for y (I would use the third original equation since it has only x and y in it)