SOLUTION: what are the two coordinates for the problem below: 3x+6y=6 2x-3y=4

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Question 68974: what are the two coordinates for the problem below:
3x+6y=6
2x-3y=4

Found 2 solutions by checkley75, funmath:
Answer by checkley75(3666) About Me  (Show Source):
You can put this solution on YOUR website!
3x+6y=6
6y=-3x+6
y=-3x/6+6/6
y=-x/2+1
------------------------
2x-3y=4
-3y=-2x+4
y=-2x/3+4/3
+graph%28+300%2C+200%2C+-6%2C+5%2C+-10%2C+10%2C+y+=+-x%2F2+%2B1%2C+y+=+-2x%2F3+%2B4%2F3%29+ (graph 300x200 pixels, x from -6 to 5, y from -10 to 10, of TWO functions y = -x/2 +1 and y = -2x/3 +4/3).

Answer by funmath(2873) About Me  (Show Source):
You can put this solution on YOUR website!
what are the two coordinates for the problem below:
3x+6y=6
2x-3y=4
Multiply the bottom equation by 2 and add the two equations together to eliminate your y's then solve for x:
2(2x-3y=4)---> 4x-6y=8
:
3x+6y=6
4x-6y=8
-------
7x+0=14
7x=14
7x/7=14/7
x=2
Now substitute 2 in for x and solve for y in either equation:
3(2)+6y=6
6+6y=6
6-6+6y=6-6
6y=0
6y/6=0/6
y=0
The solution is (x,y)=(2,0)
To check substitute 2 in for x and 0 in for y and see if the equations equal out.
3(2)+6(0)=6
6+0=6
6=6 the first equation checks.
4(2)-6(0)=8
8-0=8
8=8 the second equation checks also.
Happy Calculating!!!!