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Question
2x − y = 17
3x + 5y = 6
Solution
\[\text{ Given }: 2x - y = 17\]
\[ 3x + 5y = 6\]
Using Cramers Rule, we get
\[D = \begin{vmatrix} 2 & - 1 \\3 & 5 \end{vmatrix} = 10 + 3 = 13\]
\[ D_1 = \begin{vmatrix} 17 & - 1 \\ 6 & 5 \end{vmatrix} = 85 + 6 = 91\]
\[ D_2 = \begin{vmatrix} 2 & 17 \\ 3 & 6 \end{vmatrix} = 12 - 51 = - 39\]
Now,
\[x = \frac{D_1}{D} = \frac{91}{13} = 7\]
\[y = \frac{D_2}{D} = \frac{- 39}{13} = - 3\]
\[ \therefore x = 7\text{ and }y = - 3\]
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