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
