Answer to Question #176972 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.

5x - Ky = 6

-2x + 2Ky = -3

Answer 1

Given,

5x - Ky = 6

-2x + 2Ky = -3

Now comparing the above equation with the general equation,

$ax+by=c$

$a_1=5, b_1=-k, c_1=6$

$a_2=-2, b_2=2k, c=-3$

Now, substituting the values,

$x=\frac{b_2c_1-b_1c_2}{b_2a_1-b_1a_2}$

$=\frac{12k-3k}{10k-2k}$

$=\frac{9k}{8k}$

$=\frac{9}{8}$

$y=\frac{a_2c_1-a_1c_2}{a_2b_1-a_1b_2}$

Now, again substituting the values,

$y=\frac{-12+15}{2k-10k}$

$=\frac{3}{-8k}$