SOLUTION: What is the GREATEST possible number of solutions to the following system of equations? x^2+y^2=9 9x+2y=16 a)1 b)2 c)3 d)4

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Question 1039550: What is the GREATEST possible number of solutions to the following system of equations?
x^2+y^2=9
9x+2y=16
a)1
b)2
c)3
d)4
Found 2 solutions by Edwin McCravy, solver91311:
Answer by Edwin McCravy(20065)   (Show Source): You can put this solution on YOUR website!

The first equation is that of a circle.
The second equation is that of a line.

A line can intersect a circle in at most two points.

Answer: (b) 2

Edwin
Answer by solver91311(24713)   (Show Source): You can put this solution on YOUR website!


One equation is a circle, and the other is a straight line. A circle and a straight line can intersect in 0, 1, or 2 points. The two particular equations that you provided do, in fact, intersect in two points.

A more general question and one that would better illustrate the concept that I think your instructor was trying to communicate would be:

What is the greatest number of solutions to the following system of equations:





where is any real constant > 0.

The answer is the same, but the general case illustrates all three possibilities.

John

My calculator said it, I believe it, that settles it
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