Question

Identify the determinants for the given

Answer 1

Explanation:

The first determinant is that of the matrix of coefficients:

$|A|=\left|\begin{array}{cc}5&2\\-3&-5\end{array}\right|=(5)(-5)-(-3)(2)=-19$

The second determinant is the same as the above but with the constants substituted for the x-coefficients.

$|A_x|=\left|\begin{array}{cc}14&2\\3&-5\end{array}\right|=(14)(-5)-(3)(2) =-76$

The third determinant is the same as the first but with the constants substituted for the y-coefficients.

$|A_y|=\left|\begin{array}{cc}5&14\\-3&3\end{array}\right|=(5)(3)-(-3)(14)=57$

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The solution to the system of equations is then ...

$x=\dfrac{|A_x|}{|A|}=\dfrac{-76}{-19} =4\\\\y=\dfrac{|A_y|}{|A|}=\dfrac{57}{-19} =-3$