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Question
5x + 7y = − 2
4x + 6y = − 3
Solution
\[\text{ Given }: \hspace{0.167em} 5x + 7y = - 2\]
\[ 4x + 6y = - 3\]
Using Cramer's Rule, we get
\[D = \begin{vmatrix} 5 & 7 \\4 & 6 \end{vmatrix} = 30 - 28 = 2\]
\[ D_1 = \begin{vmatrix} - 2 & 7\\ - 3 & 6 \end{vmatrix} = - 12 + 21 = 9\]
\[ D_2 = \begin{vmatrix} 5 & - 2 \\4 & - 3 \end{vmatrix} = - 15 + 8 = - 7\]
Now,
\[x = \frac{D_1}{D} = \frac{9}{2}\]
\[y = \frac{D_2}{D} = \frac{- 7}{2}\]
\[ \therefore x = \frac{9}{2}\text{ and }y = \frac{- 7}{2}\]
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