May someone please help me

Solve this system of equation using any method.check each solution possible.
2x+3y=9
-3x+3y=-6
please help me i really don't get this problem.And again thank you very much.

2x + 3y = 9 equation 1
-3x + 3y = -6 equation 2
Subtract equation 2 from equation 1 to get:
2x + 3y - (-3x + 3y) = 9 - (-6)
2x + 3y + 3x - 3y = 15
5x = 15
x = 3
Now substitute x's value in either equation 1 or equation 2:
2(3) + 3y = 9
6 + 3y = 9
3y = 3
y = 1
So the solution is x = 3 and y = 1
Substitute x = 3 and y = 1 into equation 1 to check:
2(3) + 3(1) = 6 + 3 = 9
Substitute x = 3 and y = 1 into equation 2 to check:
-3(3) + 3(1) = -9 + 3 = -6

first pick a variable and get rid of it...since 3y is the same, eliminate that one. but in order to eliminate it, it has to be opposite...so multiply one set by 1 and the other set by -1:

1(2x+3y=9) = 2x+3y=9
-1(-3x+3y=-6) =3x-3y=6

right so now that u have opposites, get rid of the y variable
so now u shud have:

2x=9
3x=6

now add:

5x=15

divide:

x=3

right...now substitute to get y:

2(3)+3y=9

solve:

6+3y=9

3y=3

y=1

(3,1)

and u can double check by substituting with the 2nd equation...im lazy so i cant be bothered...lol

x=3 y=1

Multiply the bottom equation by -1 which gives you 3x-3y=6. Combine the equations and the y variables cancel giving you 5x=15 Divide each side by 5 and you get x=3. Next plug in the x and solve the equation and you end up with y=1

Use elimination by multiplying the second eq. by(-1) and adding it to the first

2x+3y=9
3x -3y=6
-----------
5x=15

x=3

Substitute x in any eq to find y

2(3)+3y=9

6+3y=9

3y=3

y=1

The solution is (3,1)

Check:

2(3)+3(1)=6+3=9

-3(3)+3(1)=-9+3=-6

i will use elimination
2x+3y=9
-3x+3y=-6

2x+3y=9
3x-3y=6

5x=15
x=3
2(3) + 3y =9
6 + 3y =9
3y=3
y=1

answer is (3,1)

2x+3y=9
-3x+3y=-6
subtractbottom from top
5x =15
x=3
sub in
2(3) +3y =9
6+3y =9
3y =3
y=1 -3(3) +3(1)=-6 -9 +3 = -6