91Ó°ÊÓ

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

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

Use the provided equations and substitute the value of a, b, c, d, e, f, g, h, i, j, k and l into role="math" localid="1647336941171" $r=\frac{\left|\begin{array}{ccc}j& b& c\\ k& e& f\\ l& h& i\end{array}\right|}{\left|\begin{array}{ccc}a& b& c\\ d& e& f\\ g& h& i\end{array}\right|}$after it perform simplification of determinants to write the value of r.

$\begin{array}{c}r=\frac{\left|\begin{array}{ccc}10& 4& 3\\ 15& −2& 1\\ −1& 2& −3\end{array}\right|}{\left|\begin{array}{ccc}1& 4& 3\\ 2& −2& 1\\ 1& 2& −3\end{array}\right|}\\ =\frac{300}{50}\\ =6\end{array}$

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

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

Use the provided equations and substitute the value of a, b, c, d, e, f, g, h, i, j, k and l into role="math" localid="1647337080021" $s=\frac{\left|\begin{array}{ccc}a& j& c\\ d& k& f\\ g& l& i\end{array}\right|}{\left|\begin{array}{ccc}a& b& c\\ d& e& f\\ g& h& i\end{array}\right|}$after it perform simplification of determinants to write the value of s.

$\begin{array}{c}s=\frac{\left|\begin{array}{ccc}1& 10& 3\\ 2& 15& 1\\ 1& −1& −3\end{array}\right|}{\left|\begin{array}{ccc}1& 4& 3\\ 2& −2& 1\\ 1& 2& −3\end{array}\right|}\\ =\frac{−25}{50}\\ =−\frac{1}{2}\end{array}$

Apply the Cramer’s rule for the value of t.

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

Use the provided equations and substitute the value of a, b, c, d, e, f, g, h, i, j, k and l into role="math" localid="1647337225319" $t=\frac{\left|\begin{array}{ccc}a& b& j\\ d& e& k\\ g& h& l\end{array}\right|}{\left|\begin{array}{ccc}a& b& c\\ d& e& f\\ g& h& i\end{array}\right|}$after it perform simplification of determinants to write the value of t.

$\begin{array}{c}s=\frac{\left|\begin{array}{ccc}1& 4& 10\\ 2& −2& 15\\ 1& 2& −1\end{array}\right|}{\left|\begin{array}{ccc}1& 4& 3\\ 2& −2& 1\\ 1& 2& −3\end{array}\right|}\\ =\frac{100}{50}\\ =2\end{array}$

The obtained value of r is 6, s is $-\frac{1}{2}$ and t is 2 so the solution is $\left(6,-\frac{1}{2},2\right)$.