Given two lines: 5x + 2y = 6, and 3x - ay = 4

Which value of a makes given lines parallel to each other?

1 / Let's isolated y for both equations

5x + 2y = 6 becomes y = - 5/2x + 3

3x - ay = 4 becomes y = 3/ax - 4/a

2 / The slope of each lines is m, which is the coefficient in front of the x (here - 5/2x & 3/a x)

3 / So we just need to solve for these 2 coefficient (m) being equal in order for the 2 lines to be parallel.

meaning we want to find a for : - 5/2 x = 3/a x

4 / Let's solve then:

cancel out the two x on each side

-5/2 = 3/a

isolate a:

a = - 6/5