What is the value of x, y, and z in the solution of the system of linear equations?
{x + y + z = 4 2x - 2y - z = 3 - 4x + y + 2z = -3

x=2, y=-1, z=3

Step-by-step explanation:

The system shown in the attached picture can be solved using any method you wish

I think that the best way to go is by using the subtraction method,

First multiply the equation x+y+z=4 by 2, then sum it to the second equation.

This gives another equation: 4x+z=11.

If we subtract the first eq. with the third, we have another eq. -5x+z=-7.

Lest sum the 2 new founded equations, to obtain the following result: -9x=-18

thus, we obtain x=2

Next lets go backwards in the prior eq -5x+z=-7, with x=2, we obtain that z=3

Now in the first equation (x+y+z=4) we can substitute x=2, z=3 to obtain y value.