How do i find the solution to this system? step by step, : ) {3x + 3y = 10 {-9x + 9y = -30

3X+3Y=10
-9X+9Y=30

First i notice we can get rid of X if we multiply the entire first equation by 3 so it makes it easier to add the equations toogether and get rid of X 
3(3X+3Y=10)
9X+9Y=30

Next we will add this new equation (9X+9Y=30) to the other equation (-9X+9Y=30)

9X+9Y=30
        +
-9X+9Y=30

18Y=60
Then we divide both sides by 18
18Y=60
/18   /18
Y=3.3333333
Last we substitute Y=3.333 into one of the two equations to find X value
3X+3Y=10
3X+3(3.33)=10
Finally we solve for X
3X+3(3.33)=10
3X+10=10
    -10    -10
3X=0
/3    /3
X=0

The answer could be (0,3.33)  but the more likely answer is No Solution. These two equations represent lines and when we solve a system of equations what we are really trying to find is a point where the two lines intersect, sometimes these lines do not cross paths, due to them being parallel. The way to test this is to put these two equations into Y-intercept formula (Y=mx+b) and graph them to see if they are parallel if so this system of equations has no anwser