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I have a line $y=x$ and I need to find the point $(X,Y)$ that their distance is less or equal to $7$ from the line $y=x$.

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    There is not a single point that is "less than or equal to z" from the line. There is a set of points. What does that set look like? It is a band that is 14 units wide (7 on each side of the line y=x) and the boundaries are lines parallel to $y=x.$ Can you find these lines? Can you find one point on either of these lines? Do you know how to find the distance of a point from a line? – 2017-01-27
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    yeah i know, i have to find the set of points – 2017-01-27
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    If you can find a point on the x-axis that is exactly 7 points from this line, you will have an easy formula for one side of the zone. And the other side is symmetric. Note that (1,0) is only $\frac 1{\sqrt2}$ from the line. – 2017-01-27

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The set you are searching for is bounded by two lines (let's call them $g$ and $h$) that are parallel to the line $y=x$.

So they can be represented by the formulas $$g:\ y=x+d_g$$ and $$h:\ y=x+d_h$$ You can also write that as $$d_g=y-x$$ and $$d_h=y-x$$ Without loss of generality, we can say that $g$ is below the line $y=x$ and $h$ is above the line $y=x$. This leads to $d_g < 0 < d_h$.

So the set of points you are searching for is $$\{(x,y)\mid d_g\leq y -x\leq d_h\}$$ All that needs to be done now is to calculate $d_g$ and $d_h$. I suppose that this question concerns your homework, so I will not do that for you. Just a tip: Make a drawing of the geometrical situation that I explained above and then use Pythagoras' theorem to calculate $d_g$ and $d_h$.