Explained: "Without graphing, determine if the following system has..."

Tolnaio

Answered question

2021-09-25

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

Pohanginah

Skilled2021-09-26Added 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

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