Answer to Question #176975 in Linear Algebra for william

Question

use Cramer's Rule to find the solution of the systems of linear equation in terms of the parameter K.

2x - 3y = K

x + 2y = -2

Answer 1

$\Delta = \left| {\begin{matrix} 2&{ - 3}\\ 1&2 \end{matrix}} \right| = 4 + 3 = 7$

${\Delta _1} = \left| {\begin{matrix} K&{ - 3}\\ { - 2}&2 \end{matrix}} \right| = 2K - 6$

${\Delta _2} = \left| {\begin{matrix} 2&K\\ 1&{ - 2} \end{matrix}} \right| = - 4 - K$

Then

$x = \frac{{{\Delta _1}}}{\Delta } = \frac{{2K - 6}}{7}$

$y = \frac{{{\Delta _2}}}{\Delta } = \frac{{ - 4 - K}}{7}$

Answer: $x = \frac{{2K - 6}}{7}, y = \frac{{ - 4 - K}}{7}$