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Question
2x + 3y = 10
x + 6y = 4
Solution
\[\text{ Given }: 2x + 3y = 10\]
\[ x + 6y = 4\]
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,
\[x = \frac{D_1}{D} = \frac{48}{9} = \frac{16}{3}\]
\[y = \frac{D_2}{D} = \frac{- 2}{9}\]
\[ \therefore x = \frac{16}{3}\text{ and }y = \frac{- 2}{9}\]
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