Question 146809
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 + y = 8}}} Start with the given equation



{{{2x + x = 8}}} Plug in {{{y=x}}} 



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



{{{x=(8)/(3)}}} Divide both sides by {{{3}}} to isolate {{{x}}}.



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Answer:


So the answer is {{{x=8/3}}} (which also means that {{{y=8/3}}})


So the only point that is equidistant from the coordinate axes that lies on the line {{{2x + y = 8}}} is *[Tex \LARGE \left(\frac{8}{3},\frac{8}{3}\right)]