First equation - 4x + 9 y equals 9 second equation x - 3y equals negative 6 use the elimination process all of it

-4x + 9y = 9 ... A

x - 3y = - 6 ... B

Multiply B by 4. This will delete 4x.

-4x + 9y = 9

4x - 12y = - 24

-3y = - 15

y = - 15/-3

y = 5

To find x, plug y = 5 into A or B.

I will use A.

-4x + 9y = 9

-4x + 9 (5) = 9

-4x + 45 = 9

-4x = 9 - 45

-4x = - 36

x = - 36/-4

x = 9

Answer: x = 9, y = 5.