exam Maths Puzzle Numerical Ability

Solve for Z
|6-z|<7

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exam Other Question

Hello, I worked this problem and only got half credit.
How can I work this as a systems of equations
x^2+y^2=25
5=x+y
This is what I did
x=5-y
(y-5)^2+y^2=25
2y-y^2-25=0 y=x and y=x+2 Do these lines intersect when graphed?

I think I can substitute any number for x, but I'm not sure. I also do not think the lines will intersect, but I'm not sure.