Question

Using Cramer's rule to solve linear systems.

Answer 1

Answer: Last Option

`x=2,\ y=-5`

Explanation:

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

`x =(Det(A_X))/(Det(A))`

`y =(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 =(|A_X|)/(|A|) = (80)/(40)\\\\x=2`

`y =(|A_Y|)/(|A|) = (-200)/(40)\\\\y=-5`