What is the solution to the following system ?

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.

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