Question

Determine the values of \( x \) and \( y \).

Hint:

To solve for variables using \( X = A^{-1}B \): 1. Multiply the inverse matrix \( A^{-1} \) with \( B \). 2. Perform element-wise multiplication and addition.

Answer 1

Step 1: Use \( X = A^{-1}B \): \[ X = \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 0.2 & 0.1 \\ 0.125 & 0.125 \end{bmatrix} \begin{bmatrix} 80 \\ 160 \end{bmatrix}. \]
Step 2: Perform the matrix multiplication: \[ x = 0.2(80) + 0.1(160) = 16 + 16 = 32, \] \[ y = 0.125(80) + 0.125(160) = 10 + 20 = 30. \]
Final Answer: \[ x = 32, \quad y = 30. \]