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How many solutions of the system x - y = 3 and x^2 - y = 1 are there such that both x and y are real?

 
 Sep 8, 2021
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How many solutions of the system x - y = 3 and x^2 - y = 1 are there such that both x and y are real?    

 

Let's rearrange the two equations  

 

Rearrange x – y = 3      to  y = x – 3  

Rearrange x2 – y = 1    to  y = x2 – 1  

 

The answer to "How many..." is NONE.    

 

I graphed both equations on Desmos.  I tried to paste in a screenshot of the curves, but couldn't figure out how.   

 

y = x2 – 1 is an upward opening parabola that crosses the y-axis at (0,–1)  

y = x – 3   is a straight line that passes beneath the parabola and crosses the y-axis at (0,–3)  

 

The two curves never intersect each other, so they have no solutions in common.  

.

 
 Sep 9, 2021
edited by Guest  Sep 9, 2021

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