Algebra

First, let's make some observations about this question. 

All points 5 units away from point (2, 7) would make a circle with center (2, 7) and radius 5. 

The formula for that circle would look something like \((x-2)^2+(y-7)^2=25\)

 

Now, combining that with the second equation, and we get a system. 

Subsituting out y with the x values in the line equation, we get

\((x-2)^2+(5x-35)^2=25\)

 

Simplifying, and we get

\(13x^{2}-177x+602=0\)

 

Using the quadratic equation, we find two values of x. We get

\(x=7\\ x=\frac{86}{13}\)

 

Plugging these x values into the second equation where we isolated y, we get thatr \(y=7;y=\frac{66}{13}\)

 

So our final two answers are (7, 7) and (86/13, 66/13)

 

Thanks! :)