Complete the following activity to solve the simultaneous equations by Cramer's rule :\[ 2x + 3y = 12 \]\[ x - y = 1 \]Solution :\(D = \begin{vmatrix} 2 & 3 \\ 1 & -1 \end{vmatrix} = (2 \times -1) - (3 \times 1) =\) ____\(D_x = \begin{vmatrix} \text{…

Answer: \(D = -5\), \(D_x = -15\), \(D_y = -10\); \(x = 3,\ y = 2\)

\(D = \begin{vmatrix} 2 & 3 \\ 1 & -1 \end{vmatrix} = (2)(-1) - (3)(1) = -2 - 3 = -5\).

\(D_x = \begin{vmatrix} 12 & 3 \\ 1 & -1 \end{vmatrix} = (12)(-1) - (3)(1) = -12 - 3 = -15\).

\(D_y = \begin{vmatrix} 2 & 12 \\ 1 & 1 \end{vmatrix} = (2)(1) - (12)(1) = 2 - 12 = -10\).

\(x = \dfrac{D_x}{D} = \dfrac{-15}{-5} = 3\), \(y = \dfrac{D_y}{D} = \dfrac{-10}{-5} = 2\).

Check: \(2(3) + 3(2) = 12\) and \(3 - 2 = 1\). Blanks in order: −5, 12, 1, 3, 2.