Question

Solve the following simultaneous equations using Cramer's rule.
(ii) 4x + 3 y $-$ 4 = 0 ; 6 x = 8 $-$ 5y

Answer 1

The given equations are:

4x + 3 y $-$ 4 = 0
⇒ 4x + 3 y = 4 ----------(i)
and
6 x = 8 $-$ 5y
⇒ 6 x + 5y = 8 ----------(ii)

Here, D = $\left|\begin{array}{cc}4& 3\\ 6& 5\end{array}\right|=4\times 5-3\times 6=20-18=2$
Now, we have:
D_x =$\left|\begin{array}{cc}4& 3\\ 8& 5\end{array}\right|=4\times 5-3\times 8=20-24=-4$

D_y =$\left|\begin{array}{cc}4& 4\\ 6& 8\end{array}\right|=4\times 8-4\times 6=32-24=8$

By Cramer's rule, we get:

$$\begin{gathered} x=\frac{D_x}{D}=\frac{-4}{2}=-2 \\ \mathrm{and} \\ y=\frac{Dy}{D}=\frac{8}{2}=4 \\ \therefore x=-2\mathrm{and}y=4\mathrm{is}\mathrm{the}\mathrm{solution}\mathrm{of}\mathrm{the}\mathrm{given}\mathrm{simultaneous}\mathrm{equations}. \end{gathered}$$