Question

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

Answer 1

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)