Without graphing, determine if the following system has no solution or infinitel

Tolnaio 2021-09-25 Answered
Without graphing, determine if the following system has no solution or infinitely many solutions.
(x+2)2+(y1)25
(x+2)2+(y1)25
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Expert Answer

Pohanginah
Answered 2021-09-26 Author has 96 answers
Step 1
We see that the right and left side of the inequalities are same. Only the sign between them were different.
Both equations have (x+2)2+(y1)2=5 in common.
Step 2
So any (x,y) satisfying the equation (x+2)2+(y1)2=5 will be in the solution set.
(x+2)2+(y1)2=5 is an equation of circle with center =(2,1) and radius =5. There are infinitely many points which lie on the circle. This means there are infinitely many solutions.
Answer: Infinitely many solutions
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