Answer
$det(A)=-7x+3y-8$
Work Step by Step
$ \begin{bmatrix}
x & y & 1 \\
-2 & -2 & 1 \\
1& 5 & 1
\end{bmatrix} $
$M_{11}= \begin{bmatrix}
-2 &1 \\
5& 1\\
\end{bmatrix} = -2\times1-5(1)=-7$
$M_{12}= \begin{bmatrix}
-2&1\\
1& 1\\
\end{bmatrix}=-2\times1-1\times1=-3$
$M_{13}= \begin{bmatrix}
-2 &-2 \\
1& 5\\
\end{bmatrix}= -2\times5-1(-2)=-8$
To calculate the cofactors, use the cofactor definition: $C_{ij}=(-1)^{ij}\times M_{ij}$
$C_{11}=-7$
$C_{12}=3$
$C_{13}=-8$
$det(A)=a_{11}C_{11}+a_{12}C_{12}+a_{13}C_{13}$
$det(A)=x\times(-7)+y\times3-1\times(-8)$
$det(A)=-7x+3y-8$