Question

Solve the following simultaneous equations by using Cramer's Rule
$3x+y=1$,
$2x-11y=3$

Answer 1

The given simultaneous equations are
$3x+y=1$ ....... (1)
$2x-11y=3$ ........ (2)
$D=\left|\begin{array}{cc}3& 1\\ 2& -11\end{array}\right|$
$=3\times (-11)-1\times 2$
$=-33-2=-35$
$D_x=\left|\begin{array}{cc}1& 1\\ 3& -11\end{array}\right|$
$=1\times (-11)-1\times 3$
$=-11-3=-14$
$D_y=\left|\begin{array}{cc}3& 1\\ 2& 3\end{array}\right|$
$=3\times 3-1\times 2=9-2=7$
$\therefore$ By Cramer's rule, we get
$x=\frac{D_x}{D}=\frac{-14}{35}=-\frac{2}{5}$ and $y=\frac{D_y}{D}=\frac{7}{35}=\frac{1}{5}$