Question 256387
One way you could do it is to explicitly solve for both x and y and then just add their squares. However, here's another way to do this problem.



{{{y = 15/x}}} Start with the second equation.



{{{xy = 15}}} Multiply both sides by x.



{{{2xy = 30}}} Multiply both sides by 2.



{{{x + y = 11}}} Move back to the first equation.



{{{(x + y)^2 = (11)^2}}} Square both sides



{{{(x + y)^2 = 121}}} Square 11 to get 121



{{{x^2+2xy+y^2 = 121}}} FOIL



{{{x^2+30+y^2 = 121}}} Plug in {{{2xy = 30}}} (this is why I manipulated the second equation)



{{{x^2+y^2 = 121-30}}} Subtract 30 from both sides.



{{{x^2+y^2 = 91}}} Subtract



So the solution is {{{x^2+y^2 = 91}}}