How many solutions does the system of equations .
$| x | + | y | = 1, x^{2} + y^{2} = a^{2}$ possess?

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Solution

first equation forms a square
second one forms a circle

if $0 < a < 1 / 2^{1 / 2}$ then there is no solution

if $1 / 2^{1 / 2} < a < 1$ then there are 4 solutions

of $a > 1$ then there is no solution

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How many solutions does the system of equations .|x|+|y|=1,x2+y2=a2 possess?

first equation forms a square second one forms a circle if 0<a<1/21/2 then there is no solution if 1/21/2<a<1 then there are 4 solutions of a>1 then there is no solution

How many solutions does the system of equations .
$| x | + | y | = 1, x^{2} + y^{2} = a^{2}$ possess?

first equation forms a square
second one forms a circle

if $0 < a < 1 / 2^{1 / 2}$ then there is no solution

if $1 / 2^{1 / 2} < a < 1$ then there are 4 solutions

of $a > 1$ then there is no solution