Question

Solve the following simultaneous equations using Cramer's rule .
(i) 3x $-$ y = 7 ; x + 4y = 11

Answer 1

The given equations are:
3x $-$ y = 7
x + 4y = 11

Here, D = $\left|\begin{array}{cc}3& -1\\ 1& 4\end{array}\right|=3\times 4-\left(-1\right)\times 1=12+1=13$

Now, we have:
D_x =$\left|\begin{array}{cc}7& -1\\ 11& 4\end{array}\right|=7\times 4-\left(-1\right)\times 11=28+11=39$

D_y =$\left|\begin{array}{cc}3& 7\\ 1& 11\end{array}\right|=3\times 11-7\times 1=33-7=26$

By Cramer's rule, we get:

$$\begin{gathered} x=\frac{D_x}{D}=\frac{39}{13}=3 \\ \mathrm{and} \\ y=\frac{Dy}{D}=\frac{26}{13}=2 \\ \therefore x=3\mathrm{and}y=2\mathrm{is}\mathrm{the}\mathrm{solution}\mathrm{of}\mathrm{the}\mathrm{given}\mathrm{simultaneous}\mathrm{equations}. \end{gathered}$$