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Question
9x + 5y = 10
3y − 2x = 8
Solution
\[\text{ Given }: 9x + 5y = 10 \]
\[ 3y - 2x = 8 \]
Rearranging the second equation, the two equations can be written as
\[ 9x + 5y = 10\]
\[ - 2x + 3y = 8\]
Now,
\[D = \begin{vmatrix} 9 & 5\\ - 2 & 3 \end{vmatrix} = 27 + 10 = 37\]
\[ D_1 = \begin{vmatrix} 10 & 5\\ 8 & 3 \end{vmatrix} = 30 - 40 = - 10\]
\[ D_2 = \begin{vmatrix} 9 & 10 \\ - 2 & 8 \end{vmatrix} = 72 + 20 = 92\]
Using Cramer's rule, we get
\[x = \frac{D_1}{D} = \frac{- 10}{37}\]
\[y = \frac{D_2}{D} = \frac{92}{37}\]
\[ \therefore x = \frac{- 10}{37}\text{ and }y = \frac{92}{37}\]
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