SOLUTION: If the solutions to the two equations below are the same, find the value of k, if x,y ϵ z. {{{ (x+7)^2+(y-3)^2=0 }}}, {{{-2x+3y=k }}}

Algebra ->  Distributive-associative-commutative-properties -> SOLUTION: If the solutions to the two equations below are the same, find the value of k, if x,y ϵ z. {{{ (x+7)^2+(y-3)^2=0 }}}, {{{-2x+3y=k }}}      Log On


   

Question 1104947: If the solutions to the two equations below are the same, find the value of k, if x,y ϵ z. +%28x%2B7%29%5E2%2B%28y-3%29%5E2=0+, -2x%2B3y=k+
Answer by ikleyn(52751) About Me  (Show Source):
You can put this solution on YOUR website!
.
First equation says that the sum of two squares is equal to zero.


It may happen if and only if each square is equal to zero.


It implies  x= -7,  y= 3.


So,  x= -7,  y= 3  is the only solution to the first equation.


Next, the condition says that it is also the solution to the second equation.


It implies, by substituting the values into the second equation, that 


    k = -2*(-7) + 3*3 = 14 + 9 = 23.


Answer.  k = 23.

Solved.