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

Without graphing, determine if the following system has no solution or infinitely many solutions.
${\left(x+2\right)}^{2}+{\left(y-1\right)}^{2}\le 5$
${\left(x+2\right)}^{2}+{\left(y-1\right)}^{2}\ge 5$
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Pohanginah
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 ${\left(x+2\right)}^{2}+{\left(y-1\right)}^{2}=5$ in common.
Step 2
So any (x,y) satisfying the equation $\left(x+2\right)2+\left(y-1\right)2=5$ will be in the solution set.
${\left(x+2\right)}^{2}+\left(y-1\right)2=5$ is an equation of circle with center $=\left(-2,1\right)$ and radius $=\sqrt{5}$. There are infinitely many points which lie on the circle. This means there are infinitely many solutions.