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Question
If the pair of equations ax + 2y = 7 and 3x + by = 16 represent parallel lines, then ab = ______.
Fill in the Blanks
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Solution
If the pair of equations ax + 2y = 7 and 3x + by = 16 represent parallel lines, then ab = 6.
Explanation:
For parallel lines the slopes are equal.
From ax + 2y = 7, slope = `-a/2`.
From 3x + by = 16, slope = `-3/b`.
So `-a/2 = -3/b`
⇒ `a/2 = 3/b`
⇒ ab = 6
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