Question

Write D_x for the following simultaneous equations :
(i) 3x + 4y = 8 ; x $-$ 2y = 5

(ii) 5x = 10 $-$ 2y ; y = 3x $-$ 11

Answer 1

$$\begin{gathered} \left(\mathrm{i}\right) \\ \mathrm{We}\mathrm{have}: \\ 3x+4y=8 \\ \mathrm{and} \\ x-2y=5 \\ \therefore {\mathrm{D}}_x=\left|\begin{array}{cc}8& 4\\ 5& -2\end{array}\right| \end{gathered}$$

$$\begin{gathered} \left(\mathrm{ii}\right) \\ \mathrm{We}\mathrm{have}: \\ 5x=10-2y \\ \Rightarrow 5x+2y=10 \\ \mathrm{and} \\ y=3x-11 \\ \Rightarrow 3x-y=11 \\ \therefore {\mathrm{D}}_x=\left|\begin{array}{cc}10& 2\\ 11& -1\end{array}\right| \end{gathered}$$