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Question
2x − y = − 2
3x + 4y = 3
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Solution
\[\text{ Given }: 2x - y = - 2\]
\[ 3x + 4y = 3\]
Using Cramer's Rule, we get
\[D = \begin{vmatrix} 2 & - 1 \\3 & 4 \end{vmatrix} = 8 + 3 = 11\]
\[ D_1 = \begin{vmatrix} - 2 & - 1\\ 3 & 4 \end{vmatrix} = - 8 + 3 = - 5\]
\[ D_2 = \begin{vmatrix} 2 &- 2 \\3 & 3 \end{vmatrix} = 6 + 6 = 12\]
Now,
\[x = \frac{D_1}{D} = \frac{- 5}{11}\]
\[y = \frac{D_2}{D} = \frac{12}{11}\]
\[ \therefore x = - \frac{5}{11}\text{ and }y = \frac{12}{11}\]
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