If a = - 12/5, then 5x + 2y = 6 and 3x - ay = 4 are parallel.

5x + 2y = 6

Add - 2y to both sides

5x = - 2y + 6

Divide both sides by 5

x = - 2 / 5 y + 6/5

that into the second equation:

3 ( - 2 / 5 y + 6/5 ) + 12/5 y = 4

simplify

6/5 y + 18/5 = 4

Add (-18) / 5 to both sides

6/5 y = 2 / 5

divide both sides by 6/5

y = 1/3

substitute 1/3 for y in x = - 2/5y + 6/5 to solve for x

x = - 2/5 (1/3) + 6/5

x = 16/15

so x = 16/15 and y = 1/3

now replace both x and Y in each of the original equations to check the answers:

5 (16/15) + 2 (1/3) = 5 1/3 + 2/3 = 6 true

3 (16/15) - - 12/5 (1/3) = 4 true

so they are parallel