I took a test in math to determine where I was etc etc...(adsbygoogle = window.adsbygoogle || []).push({});

anyways, the following question came up:

How many answers are there to the following system of equations?

x^2 + 5y = 30

x^2 + (y-3)^2 = 9

a) 0

b) 1

c) 2 (my answer)

d) 3 (correct answer)

The first thing I noticed was that x was the same thing in both cases, the answer would not be changed because of it. As such, x could be almost any value (infinite answers). So obviously, they wanted how many solutions for Y.

My work (in my head) was:

x^2 + 5y = 30

x^2 + (y-3)^2 = 9

*subtract equations from each other

5y - (y-3)^2 = 21

*break (y-3)^2

5y - (y^2 - 6y + 9) = 21

5y - y^2 + 6y - 9 = 21

11y - y^2 = 30

*place ^2 in positive and use ax^2 + bx + c format

y^2 - 11y + 30 = 0

*check for 2 or 1 answers by checking if the sqr() portion of quadratic formula is non zero

sqr(121 - 4*30*1) = sqr(1) = 1

since 1 <> 0, and the answer will be +- 1, there are two answers.

Where is my mistake?

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# What's wrong here?

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