plaverbach wrote:

Can this be solved visually??

1) as a circle on the xy plane

OR

2) as a tringle(pitagoras)

yes it can be solved by co-ordinate geometry.

x^2 + y^2 = 100

is a circle with radius 10

A. |x| + |y|=10 are four lines which intersect the circle at (10,0),(0,10),(-10,0)&(0,-10)

B. |x|>|y| there are multiple such points I have marked one such in the attached picture

C. This is an area outside the circle. The closest to the circle is at y=0 even here x is outside the area of the circle. A suggestion that when we look at inequalities in co-ordinate geometry think in terms of area.

D. |x|=|y| essentially two lines y=x and y=-x

E. |x| - |y|=5 they are four lines again

Attaching a very crude diagram. Apologies.

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Regards

J

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