Step 1: Add Equation 2 and Equation 3 to eliminate z.
(-x + y - z) + (x - 3y) = -1 + 3
y - 4y = 2
-3y = 2
y = -2/3
Step 2: Substitute the value of y (-2/3) into Equation 3 to find the value of x.
x - 3(-2/3) = 3
x + 2 = 3
x = 1
Step 3: Substitute the values of x and y into Equation 1 to find the value of z.
3(1) - 8(-2/3) + z = 8
3 + 16/3 + z = 8
9/3 + 16/3 + z = 8
25/3 + z = 8
z = 8 - 25/3
z = 24/3 - 25/3
z = -1/3
Therefore, the solution to the system of equations is:
x = 1
y = -2/3
z = -1/3