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Question
x − 2y = 4
−3x + 5y = −7
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Solution
\[Given: x - 2y = 4\]
\[ - 3x + 5y = - 7\]
Using the properties of determinants, we get
\[D = \begin{vmatrix} 1 & - 2\\ - 3 & 5 \end{vmatrix}= 5 - 6 = - 1 \neq 0\]
\[ D_1 = \begin{vmatrix} 4 & - 2 \\- 7 & 5 \end{vmatrix}= 20 - 14 = 6\]
\[ D_2 = \begin{vmatrix} 1 & 4\\- 3 & - 7 \end{vmatrix} = - 7 + 12 = 5\]
Using Cramer's Rule, we get
\[x = \frac{D_1}{D} = \frac{6}{- 1} = - 6\]
\[y = \frac{D_2}{D} = \frac{5}{- 1} = - 5\]
\[ \therefore x = - 6\text{ and }y = - 5\]
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