Point and a line

Yes sort of. It's similar to the bit next to the first graph, under the sub-heading "Use substitution".

Can you finish it off and solve for x?
 
Substitute y=6x+3 into x+6y=18 and you get:
x + 6(6x+3) = 18.

Can you now solve this equation for x?
 
Yes.
37x =0
x=0

So that means that x=0 at the point where the lines y=6x+3 into x+6y=18 intersect.

Now seeing that you know x=0, what is y?
 
Don't lose the bigger picture.
You are finding the point of intersection of the two lines y=6x+3 into x+6y=18.
By solving the equations simultaneously (by substitution) you have found that x=0 and y=3.
So what is the point of intersection?
 
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