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How many real solutions exist for this system of equations?

y = x2 + 4

y = 4x

 A. zero

 B. one

 C. two

 D. infinite

 Apr 14, 2023
 #1
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How many real solutions exist for this system of equations?

y = x2 + 4

y = 4x

 A. zero

 B. one

 C. two

 D. infinite

 

Assuming that x2 means x2.... 

 

Since they both equal y, we can set          x2 + 4 = 4x 

 

Subtracting 4x from boths sides we get     x2 - 4x + 4 = 0 

 

This is a quadratic which will factor to       (x - 2)(x - 2) = 0 

 

Now here's where language gets tricky. 

A quadratic has two solutions, but in this case both solutions are x = 2. 

 

So, is that considered one solution or two?  I'd say one, because the curve touches zero at only one point, but semantics might determine what it is supposed to be called.  I don't know if mathematics has a conventional nomenclature for this. 

. 

 Apr 14, 2023

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