Question

2x + 3y = 10
x + 6y = 4

Answer 1

\[\text{ Given }: 2x + 3y = 10\] 
\[ x + 6y = 4\] 
Using Cramer's Rule, we get 
\[D = \begin{vmatrix} 2 & 3\\1 & 6 \end{vmatrix} = 12 - 3 = 9\]
\[ D_1 = \begin{vmatrix} 10 & 3\\4 & 6 \end{vmatrix} = 60 - 12 = 48\] 
\[ D_2 = \begin{vmatrix} 2 & 10\\1 & 4 \end{vmatrix} = 8 - 10 = - 2\] 
Now, 
\[x = \frac{D_1}{D} = \frac{48}{9} = \frac{16}{3}\] 
\[y = \frac{D_2}{D} = \frac{- 2}{9}\] 
\[ \therefore x = \frac{16}{3}\text{ and }y = \frac{- 2}{9}\]