Question

Solve the following simultaneous equations using Cramer's rule .
(vi) 3x + y = 1 ; 2 x = 11y + 3

Answer 1

The given equations are:

3x + y = 1----------(i)
and
2 x = 11y + 3
⇒ 2 x $-$ 11y = 3 ----------(ii)

Here, D = $\left|\begin{array}{cc}3& 1\\ 2& -11\end{array}\right|=3\times \left(-11\right)-1\times 2=-33-2=-35$

Now, we have:
D_x =$\left|\begin{array}{cc}1& 1\\ 3& -11\end{array}\right|=1\times \left(-11\right)-1\times 3=-11-3=-14$


D_y =$\left|\begin{array}{cc}3& 1\\ 2& 3\end{array}\right|=3\times 3-1\times 2=9-2=7$

By Cramer's rule, we get:

$$\begin{gathered} x=\frac{D_x}{D}=\frac{-14}{-35}=\frac{2}{5} \\ \mathrm{and} \\ y=\frac{Dy}{D}=\frac{7}{-35}=\frac{-1}{5} \\ \therefore x=\frac{2}{5}\mathrm{and}y=\frac{-1}{5}\mathrm{is}\mathrm{the}\mathrm{solution}\mathrm{of}\mathrm{the}\mathrm{given}\mathrm{simultaneous}\mathrm{equations}. \end{gathered}$$