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

Question

Tolnaio 2021-09-25 Answered

Without graphing, determine if the following system has no solution or infinitely many solutions.

{(x + 2)}^{2} + {(y - 1)}^{2} \leq 5

{(x + 2)}^{2} + {(y - 1)}^{2} \geq 5

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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} + {(y - 1)}^{2} = 5

in common.
Step 2
So any (x,y) satisfying the equation

(x + 2) 2 + (y - 1) 2 = 5

will be in the solution set.

{(x + 2)}^{2} + (y - 1) 2 = 5

is an equation of circle with center

= (- 2, 1)

and radius

= \sqrt{5}

. There are infinitely many points which lie on the circle. This means there are infinitely many solutions.
Answer: Infinitely many solutions

s^{2} - 4 s = 21

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(\frac{5}{8}) + (\frac{11}{12})

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4 x + \frac{3}{x} - 9 = 5

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2 x + 5 y = 13

x = 4 - 2 y

{(x . y) ∣ 2 x + 5 v = 13}

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