SOLUTION: #1. Find a point on the line 2x + y = 8 that is equidistant from the coordinate axes. How many such points are there?

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Question 146809: #1. Find a point on the line 2x + y = 8 that is equidistant from the coordinate axes. How many such points are there?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
The statement "equidistant from the coordinate axes" means that the distances from the point to the x and y axes are the same. The only time that the distances from a certain point to both axes are the same is when the x coordinate equals the y coordinate (in other words, when y=x)


2x+%2B+y+=+8 Start with the given equation


2x+%2B+x+=+8 Plug in y=x


3x=8 Combine like terms on the left side.


x=%288%29%2F%283%29 Divide both sides by 3 to isolate x.


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Answer:

So the answer is x=8%2F3 (which also means that y=8%2F3)

So the only point that is equidistant from the coordinate axes that lies on the line 2x+%2B+y+=+8 is