Question

Solve the following simultaneous equations by using Cramer's rule:
$x-2y=-18$
$2x-y=9$

Answer 1

Equations are
$x-2y=-18...\left(i\right)$
$2x-y=9...\left(ii\right)$
$D=\left|\begin{array}{cc}1& -2\\ 2& -1\end{array}\right|$
$=(18+18)=36$
$D_y=\left|\begin{array}{cc}1& -18\\ 2& 9\end{array}\right|$
$=9+36=45$
By Cramer's rule, we get
$\therefore x=\frac{D_x}{D}$
$=\frac{36}{3}=12$
and
$y=\frac{D_y}{D}$
$=\frac{45}{3}=15$
$\therefore x=12$ and $y=15$ is the solution of the given simultaneous equations.