Solve the system by the addition 4x-5y=27 3x+3y=0

The original system of equations:
4x-5y=27
3x+3y=0

Step 1: Find a 'common ground' between either both x's or both y's using multiplication of the entirety of each equation. (I will do x).
(-3)4x-5y=27
(4)3x+3y=0
You need to make one of the factors negative so that the x's are opposites. Let's do the calculations now.
-12x+15y=-81
12x+12y=0
See how one is negative 12x and one is positive 12x?

Step 2: Now we cancel out the x's to find out what y equals. This leaves us with...
15y=-81
12y=0

Step 3: Now add your like terms.
27y=-81

Step 4: Divide each side by the coefficient.
27y÷27=-81÷27

y=-3

Step 5: Now we need to find x. Take any one equation from the original. I will be using 3x+3y=0 but you can use either one. Anywhere that you see a y in the equation, substitute it for -3.

3x+3(-3)=0

Now calculate.

3x-9=0

Then you want to move the -9 to the right side of the equation by doing inverse operations.

3x-9=0
+9 +9

3x=9

Finally, subtract both sides by the coefficient.

3x÷3=9÷3

x=3

You're solution is (3,-3)

Hope this helped!