Question

Solve the system: \[ \begin{pmatrix} x \\ y \end{pmatrix} \quad \Rightarrow \quad \begin{pmatrix} 2x - 1 \\ 9 \end{pmatrix} \] Find the values of \(x\) and \(y\).

• A. \( x = 3, \, y = 9 \)
• B. \( x = 1, \, y = 9 \)
• C. \( x = 0, \, y = 9 \)
• D. \( x = 3, \, y = 4 \)

Hint:

When equating two column vectors, match and solve each component separately. Ensure the interpretation of arrows or transformations is consistent with the context.

Answer 1

The Correct Option is A

To find \( x \) and \( y \), we equate the corresponding components of the two column vectors:

From the first row: \[ x = 2x - 1 \] Simplifying: \[ -x = -1 \quad \Rightarrow \quad x = 1 \]

From the second row: \[ y = 9 \]

Therefore, the values are: \[ \boxed{x = 1, \quad y = 9.} \]

Final Answer:

\( x = 1, \; y = 9 \)