Solution Sets

Algebra Level pending

What is the solution set of the following? x 2 + y 2 − 4 x + 6 y ≤ 3 x^{2}+y^{2}-4x+6y\leq3 and x 2 − y 2 − 4 x + 6 y ≤ 3 x^{2}-y^{2}-4x+6y\leq3 .

x x : x x ∈ ( x 2 + y 2 − 4 x + 6 y ≤ 3 \in(x^{2}+y^{2}-4x+6y\leq3 ) The solution set is all real numbers The solution is the empty set x x : x x ∈ ( x 2 − y 2 − 4 x + 6 y ≤ 3 \in(x^{2}-y^{2}-4x+6y\leq3 )

Hana Wehbi by Hana Wehbi , 51, USA

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1 solution

Hana Wehbi
May 26, 2016

The only solution for this exercise is by graphing the inequalities and take the overlapping colors as we see in the following. Thus, the solution is all the points that belong to the circle of center ( 2 , − 3 (2,-3 ) and radius= 4 4 . By completing the square method, the equation of the circle will be ( x − 2 ) 2 + ( y + 3 ) 2 = 16 (x-2)^{2} + (y+3)^{2} = 16

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