Explanation:
The first determinant is that of the matrix of coefficients:
[tex]|A|=\left|\begin{array}{cc}5&2\\-3&-5\end{array}\right|=(5)(-5)-(-3)(2)=-19[/tex]
The second determinant is the same as the above but with the constants substituted for the x-coefficients.
[tex]|A_x|=\left|\begin{array}{cc}14&2\\3&-5\end{array}\right|=(14)(-5)-(3)(2) =-76[/tex]
The third determinant is the same as the first but with the constants substituted for the y-coefficients.
[tex]|A_y|=\left|\begin{array}{cc}5&14\\-3&3\end{array}\right|=(5)(3)-(-3)(14)=57[/tex]
_____
The solution to the system of equations is then ...
[tex]x=\dfrac{|A_x|}{|A|}=\dfrac{-76}{-19} =4\\\\y=\dfrac{|A_y|}{|A|}=\dfrac{57}{-19} =-3[/tex]
