91Ó°ÊÓ

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

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

Substitute 4 in place of a, 8 in place of c, 3 in place of b, $-1$ in place of d, 6 in place of e and role="math" localid="1647191885604" $-9$ in place of f into role="math" localid="1647191879882" $x=\frac{\left|\begin{array}{cc}e& b\\ f& d\end{array}\right|}{\left|\begin{array}{cc}a& b\\ c& d\end{array}\right|}$and perform simplification of determinants to write the value of x.

$\begin{array}{c}x=\frac{\left|\begin{array}{cc}6& 3\\ −9& −1\end{array}\right|}{\left|\begin{array}{cc}4& 3\\ 8& −1\end{array}\right|}\\ =\frac{6â‹\dots \left(−1\right)−3â‹\dots \left(−9\right)}{4â‹\dots \left(−1\right)−3â‹\dots 8}\\ =\frac{21}{−28}\\ =−\frac{3}{4}\end{array}$

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

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

Substitute 4 in place of a, 8 in place of c, 3 in place of b, $-1$ in place of d, 6 in place of e and role="math" localid="1647192033998" $-9$ in place of f into role="math" localid="1647192029284" $y=\frac{\left|\begin{array}{cc}a& e\\ c& f\end{array}\right|}{\left|\begin{array}{cc}a& b\\ c& d\end{array}\right|}$and perform simplification of determinants to write the value of y.

$\begin{array}{c}y=\frac{\left|\begin{array}{cc}4& 6\\ 8& −9\end{array}\right|}{\left|\begin{array}{cc}4& 3\\ 8& −1\end{array}\right|}\\ =\frac{4â‹\dots \left(−9\right)−6â‹\dots 8}{4â‹\dots \left(−1\right)−3â‹\dots 8}\\ =\frac{−84}{−28}\\ =3\end{array}$

The obtained value of x is $-\frac{3}{4}$ and y is 3 so the solution is $\left(-\frac{3}{4},3\right)$.