Finding x and y

Solution:

Step 1: Add the matrices on LHS

\[ = \begin{bmatrix} x-y+3 & 2+(-2) & -2+2 \\ 4+1 & x+0 & 6+(-1) \end{bmatrix} = \begin{bmatrix} x-y+3 & 0 & 0 \\ 5 & x & 5 \end{bmatrix} \]

Step 2: Compare corresponding elements

From first row: \[ x – y + 3 = 6 \Rightarrow x – y = 3 \quad …(1) \] From second row: \[ x = 2x + y \Rightarrow -x = y \Rightarrow y = -x \quad …(2) \]

Step 3: Solve equations

Substitute \(y = -x\) in (1): \[ x – (-x) = 3 \Rightarrow 2x = 3 \Rightarrow x = \frac{3}{2} \] \[ y = -\frac{3}{2} \]

Final Answer:

\[ x = \frac{3}{2}, \quad y = -\frac{3}{2} \]