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

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

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

Tolnaio
2021-09-25
Answered

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

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

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

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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

We see that the right and left side of the inequalities are same. Only the sign between them were different.

Both equations have

Step 2

So any (x,y) satisfying the equation

Answer: Infinitely many solutions

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Select the correct choice below and fill in any answer boxes in your choice.

A. The solution is ___ .

(Simplify your answer. Use integers or fractions for any numbers in theexpression. Type an ordered pair.)

B. There are infinitely many solutions. The solution set is$\{(x.y)\mid 2x+5v=13\}$ .

C. There is no solution.

Select the correct choice below and fill in any answer boxes in your choice.

A. The solution is ___ .

(Simplify your answer. Use integers or fractions for any numbers in theexpression. Type an ordered pair.)

B. There are infinitely many solutions. The solution set is

C. There is no solution.