Question

If \[ \begin{bmatrix} x + y + z \\ x + y \\ y + z \end{bmatrix} = \begin{bmatrix} 9 \\ 5 \\ 7 \end{bmatrix} \] then the value of \((x, y, z)\) is:

• A. (4, 3, 2)
• B. (3, 2, 4)
• C. (2, 3, 4)
• D. (4, 2, 3)

Hint:

For systems with three variables, use substitution and elimination step-by-step to avoid confusion.

Answer 1

The Correct Option is C

We are given the equations:
1) \(x + y + z = 9\)
2) \(x + y = 5\)
3) \(y + z = 7\)
From equation (2), \(x + y = 5\).
From equation (1), subtract equation (2):
\((x + y + z) - (x + y) = 9 - 5\)
\(z = 4\)
From equation (3), \(y + z = 7\), substituting \(z = 4\):
\(y + 4 = 7 \Rightarrow y = 3\)
From equation (2), \(x + y = 5 \Rightarrow x + 3 = 5 \Rightarrow x = 2\)
Thus, \((x, y, z) = (2, 3, 4)\).