Question

Using Cramer's rule to solve linear systems.

Answer 1

Answer: Last Option

$x=2,\ y=-5$

Step-by-step explanation:

Cramer's rule says that given a system of equations of two variables x and y then:

$x =\frac{Det(A_X)}{Det(A)}$

$y =\frac{Det(A_Y)}{Det(A)}$

For this problem we know that:

$Det(A) = |A|=\left|\begin{array}{ccc}4&-6\\8&-2\\\end{array}\right|$

Solving we have:

$|A|= 4*(-2) -(-6)*8\\\\|A|=40$

$Det(A_X) = |A_X|=\left|\begin{array}{ccc}38&-6\\26&-2\\\end{array}\right|$

Solving we have:

$|A_X|=38*(-2) - (-6)*26\\\\|A_X|=80$

$Det(A_Y) = |A_Y|=\left|\begin{array}{ccc}4&38\\8&26\\\end{array}\right|$

Solving we have:

$|A_Y|=4*(26) - (38)*8\\\\|A_Y|=-200$

Finally

$x =\frac{|A_X|}{|A|} = \frac{80}{40}\\\\x=2$

$y =\frac{|A_Y|}{|A|} = \frac{-200}{40}\\\\y=-5$