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=‌−2/5‌y +‌ 6/5‌

that into the second equation:


3(‌−2/5‌y+‌6/5‌)+‌12/5‌y =4

simplify

‌6/5‌y+‌18/5‌ =4

Add (-18)/5 to both sides

‌6/5‌y=‌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