91Ó°ÊÓ

Apply the Cramer’s rule for the value of m.

$m=\frac{\left|\begin{array}{cc}e& b\\ f& d\end{array}\right|}{\left|\begin{array}{cc}a& b\\ c& d\end{array}\right|}$

Substitute 2 in place of a, $-4$ in place of c, $-4$ in place of b, 3 in place of d, $-1$ in place of e and role="math" localid="1647191286819" $-5$ in place of f into role="math" localid="1647191280200" $m=\frac{\left|\begin{array}{cc}e& b\\ f& d\end{array}\right|}{\left|\begin{array}{cc}a& b\\ c& d\end{array}\right|}$and perform simplification of determinants to write the value of m.

$\begin{array}{c}m=\frac{\left|\begin{array}{cc}−1& −4\\ −5& 3\end{array}\right|}{\left|\begin{array}{cc}2& −4\\ −4& 3\end{array}\right|}\\ =\frac{\left(−1\right)â‹\dots 3−\left(−4\right)â‹\dots \left(−5\right)}{2â‹\dots 3−\left(−4\right)â‹\dots \left(−4\right)}\\ =\frac{−23}{−10}\\ =\frac{23}{10}\end{array}$

Apply the Cramer’s rule for the value of n.

$n=\frac{\left|\begin{array}{cc}a& e\\ c& f\end{array}\right|}{\left|\begin{array}{cc}a& b\\ c& d\end{array}\right|}$

Substitute 2 in place of a, $-4$ in place of c, $-4$ in place of b, 3 in place of d, $-1$ in place of e and role="math" localid="1647191472584" $-5$ in place of f into role="math" localid="1647191466954" $n=\frac{\left|\begin{array}{cc}a& e\\ c& f\end{array}\right|}{\left|\begin{array}{cc}a& b\\ c& d\end{array}\right|}$and perform simplification of determinants to write the value of n.

$\begin{array}{c}n=\frac{\left|\begin{array}{cc}2& −1\\ −4& −5\end{array}\right|}{\left|\begin{array}{cc}2& −4\\ −4& 3\end{array}\right|}\\ =\frac{2â‹\dots \left(−5\right)−\left(−1\right)â‹\dots \left(−4\right)}{2â‹\dots 3−\left(−4\right)â‹\dots \left(−4\right)}\\ =\frac{−14}{−10}\\ =\frac{14}{10}\end{array}$

The obtained value of m is 5 and n is 1 so the solution is $\left(\frac{23}{10},\frac{7}{5}\right)$.