Question

Solve this linear system using determinants: 2x + 3y = 6 −8x − 3y = 12

Answer 1

Answer:

|A| =  18

|Ax| =  -54

|Ay| =  72

x =  -3

y =  4

Answer 2

$\left\{\begin{array}{ccc}2x+3y=6\\-8x-3y=12\end{array}\right\\\\A=\left[\begin{array}{ccc}2&3\\-8&-3\end{array}\right] \\\\|A|=\left|\begin{array}{ccc}2&3\\-8&-3\end{array}\right|=(2)(-3)-(-8)(3)=-6+24=18\\\\|A_x|=\left|\begin{array}{ccc}6&3\\12&-3\end{array}\right|=(6)(-3)-(12)(3)=-18-36=-54\\\\|A_y|=\left|\begin{array}{ccc}2&6\\-8&12\end{array}\right|=(2)(12)-(-8)(6)=24+48=72\\\\x=\dfrac{|A_x|}{|A|}=\dfrac{-54}{18}=-3\\\\y=\dfrac{|A_y|}{|A|}=\dfrac{72}{18}=4\\\\Answer:\ x=4,\ y=-3$