Question

Solution of the system of equations $x+18=2y,y=2x-9$ is:

• A. $x=19,y=14$
• B. $x=13,y=12$
• C. $x=12,y=15$
• D. $x=17,y=10$

Answer 1

The correct option is C $x=12,y=15$

We can rewrite the equations as:
$x-2y=-18$
$2x-y=9$

So by Cramer's rule.
$\Delta =\left|\begin{array}{cc}1& -2\\ 2& -1\end{array}\right|=3$

${\Delta }_x=\left|\begin{array}{cc}-18& -2\\ 9& -1\end{array}\right|=36$

${\Delta }_y=\left|\begin{array}{cc}1& -18\\ 2& 9\end{array}\right|=45$
Hence,
$x=\frac{{\Delta }_x}{\Delta }=\frac{36}{3}=12$

$y=\frac{{\Delta }_y}{\Delta }=\frac{45}{3}=15$