Question 930685

Please help me show a step by step solution to 
x^2+y^2=13
xy=6
<pre><font face = "Tohoma" size = 4 color = "indigo"><b>{{{x^2 + y^2 = 13}}} ------ eq (i)
{{{xy = 6}}}______{{{x = 6/y}}} ---------- eq (ii)
{{{(6/y)^2 + y^2 = 13}}} -------- Substituting {{{6/y}}} for x in eq (i)
{{{36/y^2 + y^2 = 13}}}
{{{36 + y^4 = 13y^2}}} -------- Multiplying by LCD, {{{y^2}}}
{{{y^4 - 13y^2 + 36 = 0}}}
{{{(y^2 - 4)(y^2 - 9) = 0}}}
(y - 2)(y + 2)(y -3)(y + 3) = 0
Thus: y = 2,  or   y = - 2, or   y = 3,   or    y = - 3

If y = 2
{{{x = 6/2}}}, or 3
When {{{highlight_green(system(x = 3, y = 2))}}}

If y = - 2
x = {{{6/(- 2)}}}, or - 3
When {{{highlight_green(system(x = - 3, y = - 2))}}}

If y = 3
x = {{{6/3}}}, or 2
When {{{highlight_green(system(x = 2, y = 3))}}}

If y = - 3
x = {{{6/(- 3)}}}, or - 2
When {{{highlight_green(system(x = - 2, y = - 3))}}}
You can do the check!! 
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