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, 1 in place of c, 7 in place of b, $-2$ in place of d, 4 in place of e and role="math" localid="1647188769969" $-20$ in place of f into role="math" localid="1647188762639" $m=\frac{\left|\begin{array}{cc}e& b\\ f& d\end{array}\right|}{\left|\begin{array}{cc}a& b\\ c& d\end{array}\right|}$and perform simplification of determinants to write the value of m.

$\begin{array}{c}m=\frac{\left|\begin{array}{cc}4& −7\\ −20& −2\end{array}\right|}{\left|\begin{array}{cc}2& −7\\ 1& −2\end{array}\right|}\\ =\frac{4â‹\dots \left(−2\right)−\left(−7\right)â‹\dots \left(−20\right)}{2â‹\dots \left(−2\right)−\left(−7\right)â‹\dots 1}\\ =\frac{−148}{3}\end{array}$

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, 1 in place of c, 7 in place of b, $-2$ in place of d, 4 in place of e and role="math" localid="1647188946502" $-20$ in place of f into role="math" localid="1647188941746" $n=\frac{\left|\begin{array}{cc}a& e\\ c& f\end{array}\right|}{\left|\begin{array}{cc}a& b\\ c& d\end{array}\right|}$and perform simplification of determinants to write the value of n.

$\begin{array}{c}n=\frac{\left|\begin{array}{cc}2& 4\\ 1& −20\end{array}\right|}{\left|\begin{array}{cc}2& −7\\ 1& −2\end{array}\right|}\\ =\frac{2â‹\dots \left(−20\right)−\left(4\right)â‹\dots 1}{2â‹\dots \left(−2\right)−\left(−7\right)â‹\dots 1}\\ =\frac{−44}{3}\end{array}$

The obtained value of m is $-\frac{148}{3}$ and n is $-\frac{44}{3}$ so the solution is $\left(-\frac{148}{3},-\frac{44}{3}\right)$.