91Ó°ÊÓ

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

$a=\frac{\left|\begin{array}{ccc}j& b& c\\ k& e& f\\ l& h& i\end{array}\right|}{\left|\begin{array}{ccc}a& b& c\\ d& e& f\\ g& h& i\end{array}\right|}$

Use the provided equations and substitute the value of a, b, c, d, e, f, g,

h, i, j, k and l into$a=\frac{\left|\begin{array}{ccc}j& b& c\\ k& e& f\\ l& h& i\end{array}\right|}{\left|\begin{array}{ccc}a& b& c\\ d& e& f\\ g& h& i\end{array}\right|}$after it perform simplification of

determinants to write the value of a.

$\begin{array}{c}a=\frac{\left|\begin{array}{ccc}23& 0& 1\\ −22& 7& −2\\ 34& −1& −1\end{array}\right|}{\left|\begin{array}{ccc}3& 0& 1\\ 4& 7& −2\\ 8& −1& −1\end{array}\right|}\\ =\frac{−423}{−87}\\ =\frac{141}{29}\end{array}$

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

$b=\frac{\left|\begin{array}{ccc}a& j& c\\ d& k& f\\ g& l& i\end{array}\right|}{\left|\begin{array}{ccc}a& b& c\\ d& e& f\\ g& h& i\end{array}\right|}$

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

$c=\frac{\left|\begin{array}{ccc}a& b& j\\ d& e& k\\ g& h& l\end{array}\right|}{\left|\begin{array}{ccc}a& b& c\\ d& e& f\\ g& h& i\end{array}\right|}$

Use the provided equations and substitute the value of a, b, c, d, e, f, g,

h, i, j, k and l into $c=\frac{\left|\begin{array}{ccc}a& b& j\\ d& e& k\\ g& h& l\end{array}\right|}{\left|\begin{array}{ccc}a& b& c\\ d& e& f\\ g& h& i\end{array}\right|}$after it perform simplification of

determinants to write the value of c.

$\begin{array}{c}c=\frac{\left|\begin{array}{ccc}3& 0& 23\\ 4& 7& −22\\ 8& −1& 34\end{array}\right|}{\left|\begin{array}{ccc}3& 0& 1\\ 4& 7& −2\\ 8& −1& −1\end{array}\right|}\\ =\frac{−732}{−87}\\ =\frac{244}{29}\end{array}$

The obtained value of a is$\frac{141}{29}$ , b is$−\frac{102}{29}$ and c is $\frac{244}{29}$so the solution is .$\left(\frac{141}{29},−\frac{102}{29},\frac{244}{29}\right)$