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 $0.2$ in place of a, $0.4$ in place of c, $-0.3$ in place of b, $-0.2$ in place of d, 0 in place of e and role="math" localid="1647358262642" $0.2$ in place of f into role="math" localid="1647358257862" $a=\frac{\left|\begin{array}{cc}e& b\\ f& d\end{array}\right|}{\left|\begin{array}{cc}a& b\\ c& d\end{array}\right|}$and perform simplification of determinants to write the value of a.

$\begin{array}{c}a=\frac{\left|\begin{array}{cc}0& −0.3\\ 0.2& −0.2\end{array}\right|}{\left|\begin{array}{cc}0.2& −0.3\\ 0.4& −0.2\end{array}\right|}\\ =\frac{0â‹\dots \left(−0.2\right)−\left(−0.3\right)â‹\dots 0.2}{0.2â‹\dots \left(−0.2\right)−\left(−0.3\right)â‹\dots 0.4}\\ =\frac{0.06}{0.08}\\ =0.75\end{array}$

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 $0.2$ in place of a, $0.4$ in place of c, $-0.3$ in place of b, $-0.2$ in place of d, 0 in place of e and role="math" localid="1647358620770" $0.2$ in place of f into role="math" localid="1647358584001" $b=\frac{\left|\begin{array}{cc}a& e\\ c& f\end{array}\right|}{\left|\begin{array}{cc}a& b\\ c& d\end{array}\right|}$and perform simplification of determinants to write the value of b.

$\begin{array}{c}b=\frac{\left|\begin{array}{cc}0.2& 0\\ 0.4& 0.2\end{array}\right|}{\left|\begin{array}{cc}0.2& −0.3\\ 0.4& −0.2\end{array}\right|}\\ =\frac{\left(0.2\right)â‹\dots \left(0.2\right)−0â‹\dots \left(0.4\right)}{0.2â‹\dots \left(−0.2\right)−\left(−0.3\right)â‹\dots 0.4}\\ =\frac{0.04}{0.08}\\ =0.5\end{array}$

The obtained value of a is $0.75$ and b is $0.5$ so the solution is $\left(0.75,0.5\right)$.