College

What are the values of the variables in the matrix equation?

\[
\begin{bmatrix}
9 & 1 & 8 & 3 \\
x & 1 & 6
\end{bmatrix}
=
\begin{bmatrix}
9 & 2 & y & 6 \\
1 & 6
\end{bmatrix}
\]

A. \( x = 5, y = 8 \)
B. \( x = 6, y = 3 \)
C. \( x = 3, y = 6 \)
D. \( x = 2, y = 9 \)

Answer :

Final answer:

The answer provides step-by-step instructions to solve a matrix equation with variables x and y. It explains the process clearly and shows how to find the values of x and y accurately.

Explanation:

Matrix equation: [9183x16]=[92y616]

Given matrix: [9 1; 8 3]x = [9 2; 6 1]y

To find the values of x and y, we need to solve the system of equations formed by the matrix equation.

Step-by-step:

  1. 9x + 1y = 9
    8x + 3y = 2
  2. Multiply the first equation by 3 and the second equation by 2 to eliminate y: 27x + 3y = 27 and 16x + 6y = 4
  3. Subtract the two equations: 11x = 23 → x = 2
  4. Substitute x = 2 into the first equation: 18 + y = 9 → y = -9
  5. Therefore, the values of the variables are x = 2 and y = -9.

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