Write the given equations in the form:
ax + by = c
2x + y = 19
2x – 3y = -3
\(D = \begin{vmatrix} 2&1\\2&-3\end{vmatrix}\)
\(= [2 \times(-3)] - [2 \times 1]\)
\(= -6-2\)
\(= -8\)
\(D_x = \begin{vmatrix} 19&1\\-3&-3\end{vmatrix}\)
\(= [19 \times (-3)] - [(-3) \times 1]\)
\(= -57 - (-3)\)
\(= -54\)
\(D_y = \begin{vmatrix} 2&19\\2&-3\end{vmatrix}\)
\(= [2 \times (-3) ] - [2\times19]\)
\(= -6 - 38\)
\(= -44\)
\(x = \frac{D_x}D\)
\( = \frac{-54}{-8}\)
\( = \frac{27}{4}\)
\(y = \frac{D_y}D\)
\(=\frac{-44}{-8}\)
\(=\frac{11}2\)
