Question 1034596
<pre>

Think of any number, say 1.
Substitute 1 for x in

                2x+y=6 
              2(1)+y=6
                 2+y=6
                   y=4

So one point is (x,y) = (1,4)  <-- that's one solution.



Think of any other number, say 4.
Substitute 4 for x in

                2x+y=6 
              2(4)+y=6
                 8+y=6
                   y=-2

So one point is (x,y) = (4,-2)   <-- that's another solution.


Think of any other number, say 0.
Substitute 0 for x in

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

So one point is (x,y) = (0,6)    <-- that's still another solution.

Think of any other number, say -1.
Substitute -1 for x in

                2x+y=6 
             2(-1)+y=6
                -2+y=6
                   y=8

So a fourth point is (x,y) = (-1,8)   <-- that's a fourth solution.

Plot the solutions as points:

{{{drawing(400,400,-10,10,-10,10, graph(400,400,-10,10,-10,10),


circle(-1,8,0.15),circle(-1,8,0.13),circle(-1,8,0.11),circle(-1,8,0.09),circle(-1,8,0.07),circle(-1,8,0.05),circle(-1,8,0.03),circle(-1,8,0.01),
locate(-3.5,8.5,"(-1,8)"),
locate(0+.2,6+.5,"(0,6)"),
locate(1+.2,4+.5,"(1,4)"),
locate(4+.2,-2+.5,"(4,-2)"),


circle(0,6,0.15),circle(0,6,0.13),circle(0,6,0.11),circle(0,6,0.09),circle(0,6,0.07),circle(0,6,0.05),circle(0,6,0.03),circle(0,6,0.01),

circle(1,4,0.15),circle(1,4,0.13),circle(1,4,0.11),circle(1,4,0.09),circle(1,4,0.07),circle(1,4,0.05),circle(1,4,0.03),circle(1,4,0.01),

circle(4,-2,0.15),circle(4,-2,0.13),circle(4,-2,0.11),circle(4,-2,0.09),circle(4,-2,0.07),circle(4,-2,0.05),circle(4,-2,0.03),circle(4,-2,0.01) )}}}

Now get a ruler and draw a line through them:

{{{drawing(400,400,-10,10,-10,10, graph(400,400,-10,10,-10,10),


circle(-1,8,0.15),circle(-1,8,0.13),circle(-1,8,0.11),circle(-1,8,0.09),circle(-1,8,0.07),circle(-1,8,0.05),circle(-1,8,0.03),circle(-1,8,0.01),
locate(-3.5,8.5,"(-1,8)"),
locate(0+.2,6+.5,"(0,6)"),
locate(1+.2,4+.5,"(1,4)"),
locate(4+.2,-2+.5,"(4,-2)"),

line(-12,30,12,-18),
circle(0,6,0.15),circle(0,6,0.13),circle(0,6,0.11),circle(0,6,0.09),circle(0,6,0.07),circle(0,6,0.05),circle(0,6,0.03),circle(0,6,0.01),

circle(1,4,0.15),circle(1,4,0.13),circle(1,4,0.11),circle(1,4,0.09),circle(1,4,0.07),circle(1,4,0.05),circle(1,4,0.03),circle(1,4,0.01),

circle(4,-2,0.15),circle(4,-2,0.13),circle(4,-2,0.11),circle(4,-2,0.09),circle(4,-2,0.07),circle(4,-2,0.05),circle(4,-2,0.03),circle(4,-2,0.01) )}}}

That's the graph.

Edwin</pre>