The system of equations x + 2y - z = 3, 2x - 2y + 3z = 2, 3x - y + 2z = 1 hasa)no solutionb)a unique solutionc)an infinite number of solutionsd)none of theseCorrect answer is option 'B'. Can you explain this answer?

Question

Answer

Solution:
Given system of equations are:
x + 2y - z = 3 ...(1)
2x - 2y - 3z = 2 ...(2)
3x - y + 2z = 1 ...(3)
Adding equation (1) and (2), we get:
3x - 4z = 5 ...(4)
Multiplying equation (2) by 3 and adding it to equation (3), we get:
9x - 9y = 7 ...(5)
Now, multiplying equation (1) by 3 and adding it to equation (5), we get:
11x = 16
So, x = 16/11
Substituting the value of x in equation (4), we get:
z = (3x - 5)/4 = (3(16/11) - 5)/4 = 23/44
Substituting the values of x and z in equation (1), we get:
y = (3 - x + z)/2 = (3 - 16/11 + 23/44)/2 = 5/22
Therefore, the solution of the given system of equations is:
x = 16/11, y = 5/22, z = 23/44
As the solution is unique, the correct answer is option (B).

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