Final answer:
To solve the system of equations, we substitute the given x, y, and z values and check if they satisfy the equation. The option that satisfies the equation is x = 2, y = -1, z = 0.
Step-by-step explanation:
To solve the system of equations -4x - 8y + 9z = -3a, we can use the given options to substitute x, y, and z values and check if they satisfy the equation.
a) x = -1, y = 0, z = 1:
-4(-1) - 8(0) + 9(1) = 4 + 0 + 9 = 13 ≠ -3a
Since the equation is not satisfied, option (a) is not a solution.
b) x = 2, y = -1, z = 0:
-4(2) - 8(-1) + 9(0) = -8 + 8 + 0 = 0 = -3a
Option (b) satisfies the equation for a = 0.
c) x = 0, y = 1, z = -1:
-4(0) - 8(1) + 9(-1) = 0 - 8 - 9 = -17 ≠ -3a
Since the equation is not satisfied, option (c) is not a solution.
d) x = -3, y = 2, z = 1:
-4(-3) - 8(2) + 9(1) = 12 - 16 + 9 = 5 = -3a
Option (d) satisfies the equation for a = -5/3.
Therefore, the correct solution is:
x = 2, y = -1, z = 0, a = 0 (Option b)