Answer:
Option A.
Step-by-step explanation:
The given system of the equations have been given as
5x + 2y + z = 4 -----(1)
x + 2z = 4 -------(2)
2x + y - z = -1 -----(3)
We equation 2 by 2 and subtract it from equation 3.
(2x + y - z) - 2(x + 2z) = -1 - 2(4)
2x + y - z - 2x - 4z = - 1 - 8
y - 5z = -9 -----(4)
Now we multiply equation 2 by 5 and subtract by equation 1
(5x + 2y + z) - 5(x + 2z) = 4 - 5×4
5x + 2y + z - 5x - 10z = 4 - 20
2y - 9z = -16 -----(5)
We multiply equation 4 by 2 and subtract it by equation 5
(2y - 9z) - 2(y - 5z) = -16 + 2×9
2y - 2y - 9z + 10z = -16 + 18
z = 2
Now we put z = 2 in the equation 2
x + 2×2 = 4
x + 4 = 4
x = 4 - 4
x = 0
Now we put x = 0 and z = 2 in equation 3
2×0 + y - 2 = -1
y - 2 = -1
y = -1 + 2
y = 1
Now we have the solution of the system as x = 0, y = 1 and z = 2
Option A is the answer.
