elimination

3x + 3y = 9

5x - 8y = -9

 

Multiply the top equation through by -5/3.

3(-5/3)x + 3(-5/3)y = 9(-5/3)

-5x - 5y = -15

 

Now line this up with the second equation and add straight down.

   -5x - 5y   = -15

+  5x - 8y   = -9

    0x - 13y = -24

 

-13y = -24

y = -24/-13

y = 24/13

 

Now substitute this value for y into either equation to find x.

3x + 3(24/13) = 9

3x = 9 - 72/13

3x = 45/13

x = 15/13