Intersection of inequalities problem.

[Demonoid]

I need to graph/find numbers for S∩T where S is x^2+y^2 <=100 and T is x+y<=14.

I know I can find them simply by choosing/picking them, but are there any other solution ?

I thought maybe doing

x^2+y^2 <=100
+
x+y<=14
=
x^2+y^2 + x+y<=14 +100 =
x^2+y^2 + x+y<=114 =
x^2+y^2 <= 114-x-y =
x+y <= sqrt(114-x-y) <-- doesn't work for x=7 and y=7 ?

OR am I doing something wrong ?

Venn diagram confirms that to find an intersection I need to add them and this should yield the result, but this doesn't work ? why ??

thank you for any responses !:D

 

[symbolipoint]

Graph the equations and identify points of intersection. Look for the different plane regions which the graphs form. Pick a point in each region and test if the point satisfies both equations.