Solve the following system by any method. 8x + 9y = –5 –8x – 9y = 5 a. (–10, 3) b. (–3, 10) c. (0,0) d. infinitely many solutions

I will be using the substitution method because it is my all time favorite method!

Step 1: Solve for x or y in either of the two equations. I will choose to solve for y in the equation 8x + 9y = -5 

    8x + 9y = -5 
  - 8x         + 8x

    9y = 8x - 5 
   
     9     9     9

y = 8/9x - 5/9

Step 2: Plug in the value you got for x or y into the equation that you have not worked with yet.

8x - 9(8/9x - 5/9) = 5 
8x - 8x + 5 = 5
0x + 5 = 5 
5 = 5

This turns out to be a true statement, so the answer to your system will be infinitely many solutions. 

No solution : there is no number of boxes that she bought