How do I solve this system of equations by substitution? 2x-6y=6 12y+5x=24

Question

Please help, and thank you! I would say I understand this but I got this question wrong on a algebra test, while I got all the other problems right, and can't figure out why. Thank you!

Answer 1

2x - 6y = 6

5x +12y = 24

multiply the 1st equation by 2 and add to the 2nd equation

4x - 12y = 12

5x +12y = 24

9x = 36

x = 36/9 = 4

6y = 2x -6

6y = 2(4)-6

y = 2/6 = 1/3

x = 4, y = 1/3

or

2x-6y = 6

solve for x

2x = 6y+6

x= 3y +3

substitute 3y+3 for x in the 2nd equation

5x +12y = 24

5(3y+3) +12y = 24

15y+12y = 24-15

27y = 9

y = 1/3

x=3y+3 = 3(1/3)+3= 4