We are given a system of two linear equations with two variables $x$ and $y$, and a parameter $a$. The system is $(a+2)x + (a-2)y = 16$ $2x + 4y = a-2$ We are asked to find the determinant $D$ of the coefficient matrix.

1. Problem Description

We are given a system of two linear equations with two variables $x$ and $y$, and a parameter $a$.

The system is

$(a+2)x + (a-2)y = 16$

$2x + 4y = a-2$

We are asked to find the determinant $D$ of the coefficient matrix.

2. Solution Steps

The system of equations can be written as:

$(a+2)x + (a-2)y = 16$

$2x + 4y = a-2$

The determinant $D$ of the coefficient matrix is given by:

$D = \begin{vmatrix} a+2 & a-2 \\ 2 & 4 \end{vmatrix}$

$D = (a+2)(4) - (a-2)(2)$

$D = 4a + 8 - (2a - 4)$

$D = 4a + 8 - 2a + 4$

$D = 2a + 12$

3. Final Answer

$D = 2a + 12$