91Ó°ÊÓ

Use the provided equations and 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, 2 in place of c, 1 in place of b, $-3$ in place of d, $-4$ in place of e and role="math" localid="1647244918633" $-9$ in place of f into role="math" localid="1647244913479" $x=\frac{\left|\begin{array}{cc}e& b\\ f& d\end{array}\right|}{\left|\begin{array}{cc}a& b\\ c& d\end{array}\right|}$and perform simplification of determinants to write the value of x.

$\begin{array}{c}x=\frac{\left|\begin{array}{cc}−4& 1\\ −9& −3\end{array}\right|}{\left|\begin{array}{cc}4& 1\\ 2& −3\end{array}\right|}\\ =\frac{\left(−4\right)â‹\dots \left(−3\right)−\left(1\right)â‹\dots \left(−9\right)}{4â‹\dots \left(−3\right)−\left(1\right)â‹\dots 2}\\ =\frac{21}{−14}\\ =−\frac{3}{2}\end{array}$

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, 2 in place of c, 1 in place of b, $-3$ in place of d, $-4$ in place of e and role="math" localid="1647245081200" $-9$ in place of f into role="math" localid="1647245075902" $y=\frac{\left|\begin{array}{cc}a& e\\ c& f\end{array}\right|}{\left|\begin{array}{cc}a& b\\ c& d\end{array}\right|}$and perform simplification of determinants to write the value of y.

$\begin{array}{c}y=\frac{\left|\begin{array}{cc}4& −4\\ 2& −9\end{array}\right|}{\left|\begin{array}{cc}4& 1\\ 2& −3\end{array}\right|}\\ =\frac{4â‹\dots \left(−9\right)−\left(−4\right)â‹\dots 2}{4â‹\dots \left(−3\right)−\left(1\right)â‹\dots 2}\\ =\frac{−28}{−14}\\ =2\end{array}$

The obtained value of x is $-\frac{3}{2}$ and y is 2 so the coordinates are $\left(-\frac{3}{2},2\right)$.