Karla R. answered 06/11/14
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Let Me Help You With Your Math!(Elem Math thru Pre-Calc and SAT Math)
First take x+y=14 and solve for either x or y. Then, substitute that into the other equation:
Solving for y, you get: y=-x+14
Now, substitute into x2+y2=100 ==> x2+ (-x+14)2 = 100
==> x2+ x2-28x +196 =100 (FOIL/2x2 distribution)
==>2x2-28x +96=0 (combine like terms)
==>2(x2-14x+48) =0 (GCF)
==>2(x-6)(x-8)= 0 (factor)
==> x=6 or x=8
Substitute x=6 and x=8 into y=-x+14 to find corresponding y-values:
y= -(6)+14 =8 and y= -(8)+14=6
So, points of intersection are (6,8) and (8,6)
Note: This was an equation of a circle and of a line-- the line went through the circle and intersected it at two distinct points.