How to solve this system of equations?
Real numbers x and y satisfy the system of equations
#x+y+x/y=10#
#x/y*(x+y)=20#
Determine the sum of all possible values of the expression x+y.
Real numbers x and y satisfy the system of equations
Determine the sum of all possible values of the expression x+y.
2 Answers
or
Explanation:
In the system of equations
and using quadratic formula
As
and if
(1) In first case we have
=
(2) In other case we have
=
graph{(x+y+x/y-10)(x/y(x+y)-20)=0 [-10, 10, -5, 5]}
Explanation:
Calling
solving we have
or
and
but
for
so we have finally