Solving by elimination
5x+2y= -3
3x+3y=9
me solve x and y

1) -3(5x+2y=-3)⇒ -15x-6y=9
                                             ⇒ -9x=27
     2(3x+3y=9)⇒ 6x+6y=18

2) -9x/-9=27/-9 ⇒ x=-3 

3) 3(-3)+3y=9⇒ -9+9+3y=9+9⇒ 3y/3=18/3⇒ y=6

(-3,6)

Reasoning:
Step 1) In order to eliminate, first I had to multiple the first equation by -3 and the second by 2 so that when combining the equations y would cancel each other out so that I could solve for x. Note: There are many combinations as to how you could multiple the equations so that either the x or y would cancel out.

Step 2) Once y is eliminated, solve for x.

Step 3) Now plug x back into one of the original equations and solve for y. Note: Plug x back into one of the original equations, not the equations that were changed by multiplication,