The lines 3x + by = 7 and bx + 2y = 9 are parallel to each other. What is b

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The lines 3x + by = 7 and bx + 2y = 9 are parallel to each other. Lines that are parallel to each other have the same slope. Determine the slope of the lines given.

3x + by = 7

=> y = -3x/b + 7/b

The slope of this line is -3/b.

bx + 2y = 9

=> y = (-b/2)x + 9/2

The slope of this line is -b/2

Equating -b/2 and -3/b and solving for b

-b/2 = -3/b

=> b^2 = 6

=> b = `+-sqrt 6`

The value of b is `+-sqrt 6`

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