91Ó°ÊÓ

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

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

Substitute $0.5$ in place of a, $0.75$ in place of c, $-1$ in place of b, $0.5$ in place of d, $-1$ in place of e and role="math" localid="1647192546739" $-0.25$ in place of f into role="math" localid="1647192540532" $r=\frac{\left|\begin{array}{cc}e& b\\ f& d\end{array}\right|}{\left|\begin{array}{cc}a& b\\ c& d\end{array}\right|}$and perform simplification of determinants to write the value of r.

$\begin{array}{c}r=\frac{\left|\begin{array}{cc}−1& −1\\ −0.25& 0.5\end{array}\right|}{\left|\begin{array}{cc}0.5& −1\\ 0.75& 0.5\end{array}\right|}\\ =\frac{\left(−1\right)â‹\dots 0.5−\left(−0.25\right)â‹\dots \left(−1\right)}{0.5â‹\dots 0.5−0.75â‹\dots \left(−1\right)}\\ =\frac{−0.75}{1}\\ =−0.75\end{array}$

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

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

Substitute $0.5$ in place of a, $0.75$ in place of c, $-1$ in place of b, $0.5$ in place of d, $-1$ in place of e and role="math" localid="1647192732412" $-0.25$ in place of f into role="math" localid="1647192727784" $s=\frac{\left|\begin{array}{cc}a& e\\ c& f\end{array}\right|}{\left|\begin{array}{cc}a& b\\ c& d\end{array}\right|}$and perform simplification of determinants to write the value of s.

$\begin{array}{c}s=\frac{\left|\begin{array}{cc}0.5& −1\\ 0.75& −0.25\end{array}\right|}{\left|\begin{array}{cc}0.5& −1\\ 0.75& 0.5\end{array}\right|}\\ =\frac{0.5â‹\dots \left(−0.25\right)−0.75â‹\dots \left(−1\right)}{0.5â‹\dots 0.5−0.75â‹\dots \left(−1\right)}\\ =\frac{0.625}{1}\\ =0.625\end{array}$

The obtained value of r is $-0.75$ and s is $0.625$ so the solution is $\left(-0.75,0.625\right)$.