Question 256057
 "  i need help with this: 
Find the common solution to the following pair of lines by graphing them on the same axes. 
3x + 2y = 6
x - y = 2 
The lines intersect at (?,? ). 
the answer is (2,0). i was wondering how they got (2,0). I have graphed this every way i could think of and never got (2,0). here are the answers i got: 
(-2,4), (-4,2), (2,4), (4,2), (4,-2), (2,-4), (-2,-4), (-4,-2). 
did i do that right and there's a glitch? or did i do that wrong without realizing?   "

3x+2y=6
2y=-3x+6
 y=(-3/2)x+3

x-y=2
 -y=-x+2
  y=x-2

{{{ graph( 300, 200, -10, 10, -10, 10, (-3/2)*x+3, x-2) }}}
the graph does indeed cross at (2,0)

we could also set the equations equal to one another and solve for x
(-3/2)x+3=x-2
-3x+6=2x-4
-5x=-10
  x=2

plug x=2 into each and solve for y
3x + 2y = 6
x - y = 2 

3(2)+2y=6
6+2y=6
2y=0
y=0

(2)-y=2
-y=0
y=0

I hope all this helps