SOLUTION: Hello. I was given these problems: x2(squared) + y = 16 x2(squared) + y2(squared) = 64 and told to determine whether or not this equation "defines y as a function of x." Would b

Algebra ->  Functions -> SOLUTION: Hello. I was given these problems: x2(squared) + y = 16 x2(squared) + y2(squared) = 64 and told to determine whether or not this equation "defines y as a function of x." Would b      Log On


   

Question 1022367: Hello. I was given these problems: x2(squared) + y = 16
x2(squared) + y2(squared) = 64
and told to determine whether or not this equation "defines y as a function of x." Would be very thankful for some help. Thanks for reading.
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
system%28x%5E2%2By=16%2Cand%2Cx%5E2%2By%5E2=64%29

Neither of them is specifically written as y in terms of x; but solving for y in terms of x will show you very clearly, if not otherwise understood, if each is a function or not., A vertical parabola is a function. A circle is not a function. Understand why!

Answer by ikleyn(52800) About Me  (Show Source):
You can put this solution on YOUR website!
.
Hello. I was given these problems: x2(squared) + y = 16
x2(squared) + y2(squared) = 64
and told to determine whether or not this equation "defines y as a function of x." Would be very thankful for some help. Thanks for reading.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

x%5E2+%2B+y = 16      (1)
x%5E2+%2B+y%5E2 = 64     (2)

Express x^2 = 16-y from (1) and substitute it into (2). You will get this equation for single unknown x:

%2816-y+%2B+y%5E2%29 = 64.

Simplify step by step:

y%5E2+-y+%2B+16 = 64.

y%5E2+-+y+%2B+16-64 = 0,

y%5E2+-+y+-+48 = 0.

Please complete it yourself by applying the quadratic formula.