91Ó°ÊÓ

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

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

Substitute 2 in place of a, $\frac{3}{4}$ in place of c, 3 in place of b, $-\frac{7}{8}$ in place of d, $-16$ in place of e and 10 in place of f into role="math" localid="1647241145390" $a=\frac{\left|\begin{array}{cc}e& b\\ f& d\end{array}\right|}{\left|\begin{array}{cc}a& b\\ c& d\end{array}\right|}$and perform simplification of determinants to write the value of a.

$\begin{array}{c}a=\frac{\left|\begin{array}{cc}−16& 3\\ 10& −\frac{7}{8}\end{array}\right|}{\left|\begin{array}{cc}2& 3\\ \frac{3}{4}& −\frac{7}{8}\end{array}\right|}\\ =\frac{\left(−16\right)â‹\dots \left(−\frac{7}{8}\right)−3â‹\dots 10}{2â‹\dots \left(−\frac{7}{8}\right)−3â‹\dots \left(\frac{3}{4}\right)}\\ =\frac{−16}{−4}\\ =4\end{array}$

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

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

Substitute 2 in place of a, $\frac{3}{4}$ in place of c, 3 in place of b, $-\frac{7}{8}$ in place of d, $-16$ in place of e and 10 in place of f into role="math" localid="1647241359251" $b=\frac{\left|\begin{array}{cc}a& e\\ c& f\end{array}\right|}{\left|\begin{array}{cc}a& b\\ c& d\end{array}\right|}$and perform simplification of determinants to write the value of b.

$\begin{array}{c}a=\frac{\left|\begin{array}{cc}2& −16\\ \frac{3}{4}& 10\end{array}\right|}{\left|\begin{array}{cc}2& 3\\ \frac{3}{4}& −\frac{7}{8}\end{array}\right|}\\ =\frac{2â‹\dots 10−\left(−16\right)â‹\dots \left(\frac{3}{4}\right)}{2â‹\dots \left(−\frac{7}{8}\right)−3â‹\dots \left(\frac{3}{4}\right)}\\ =\frac{32}{−4}\\ =−8\end{array}$

The obtained value of a is 4 and b is $-8$ so the solution is $\left(4,-8\right)$.