The points on the Cartesian plane (2, 3) and (3, 5) satisfy the equation:
\[ ax + by + 1 = 0 \]Then the value of \(a\) is:
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\( -2 \)
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\( 1 \)
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\( 7 \)
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\( 2 \)
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\( -1 \)
Try to solve it before checking the answer.
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\( -2 \)
Replacing the coordinates of the two points in the equation \( ax + by + 1 = 0 \) we obtain the following system:
\( \boldsymbol{(1)} \hspace{2em} 2a + 3b + 1 = 0 \)
\( \boldsymbol{(2)} \hspace{2em} 3a + 5b + 1 = 0 \)
Multiplying equation (1) by 5 and equation (2) by -3, we obtain:
\( \boldsymbol{(3)} \hspace{2em} 10a + 15b + 5 = 0 \)
\( \boldsymbol{(4)} \hspace{2em} -9a – 15b – 3 = 0 \)
Adding (4) and (5) we obtain:
\[ a + 2 = 0 \Rightarrow \boldsymbol{a = -2} \]