Step-by-step explanation:
rewriting the third equation
[tex]4x - y + z = - 5 \\ - x + y - z = 5 \\ 2x - y - z = 1[/tex]
add to second equation to the first
[tex]4x - y + z = - 5 \\ + (- x + y - z )= 5 \\ = 3x = 0 \\ x = 0[/tex]
[tex] - y + z = - 5 \\ y - z = 5 \\ - y - z = 1[/tex]
I add third equation to the second
[tex]y - z = 5 \\ + ( - y - z) = 1 \\ = - 2z = 6 \\ z = - 3[/tex]
substitute z = -3 into either one of the other two equations and solve for y
[tex] - y + ( - 3) = - 5 \\ - y - 3 = - 5 \\ - y = - 2 \\ y = 2[/tex]
x = 0
y = 2
z = -3
