If ax + 6y = 4 , 3x + by = 1 and 5x + 3y = 8 are parallel lines, what are a and b equal to?

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Parallel lines have the same slope. We have to write the given lines in the form y = mx + c, where m is the slope and c is the y-intercept.

For ax + 6y = 4

=> 6y = -ax + 4

=> y = (-a / 6) x + 4

For 3x + by =1

=> by = -3x + 1

=> y = (-3/b) x + 1/b

For 5x + 3y = 8

=> 3y = 8 – 5x

=> y = (-5/3) x + (8/5)

Now as the slope of all the three lines has to be the same -5/3 = -a/6 = -3/b

-5/3 = -a/6

=> a = 5*6/3 = 10

-5/3 = -3/b

=> b = 3*3/5

=> b = 9/5

Therefore a = 10 and b = 9/5.

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