Find the value of a so that the lines are parallel?

Question

Find the value of a so that the lines whose equations are 3x+6ay = 7 and 9ax+8y = 15 are parallel.

solution?*** thnx!

Answer 1

For two lines to be parallel, they must have the same slope. To find that, the equations must be in the format of y=mx+b. Solve for y in both equations.
3x+6ay = 7
6ay=-3x+7
y= (-3x+7)/6a
y= (-1/2a)x+7/6a

9ax+8y=15
8y=-9ax+15
y= (-9a/8)x+15/8

Set the values in the m position equal.
-1/2a = -9a/8
-18a^2=-8
a^2=4/9
a=+-2/3

Check by plugging back into the original.

Answer 2

Line 1
6ay = - 3x + 7
y = (-3/6a)x + 7/6

Line 2
8y = - 9ax + 15
y = (-9a/8)x + 15/8

(-3/6a) = (-9a/8)
1/2a = 9a/8
18a² = 8
a² = 8/18
a² = 4/9
a = ± 2/3