How to solve the system of equations algebraically for all values of x, y, and z

4x -3y + z = -10(1)
2x +y + 3z =  0(2)
-x +2y - 5z = 17(3)

First we multiply 3*(2) and add it to (1) 
6x +3y +9z =0+(1)> 10x + 10z = -10(4)

Then we multiply -2*(2) and add it to (3) 
-4x -2y -6z =0 +(3)> -5x -11z = 17(5)

Multiply  2*(5) and add it to (4)
-10x -22z = 34+(4)> -12 z = 24 >>> z = -2

Substitute z in (4)> 10x +10(-2) = -10>>> x = 1

Substitute x and z in (2)> 2(1) +y + 3(-2) =  0>>> y = 4

Solution (x,y,z) = (1,4,-2)

Idk idk idk idk idk idk idk idk