Find all order pairs #(x,y)# such that #2x^4 +5x^3 y +45xy^3 = 34x^2 y^2 + 18y^4# and #2x - 3y =7#?

1 Answer
Jun 6, 2017

#(-7,-7)# and #(14/5,-7/15)#

Explanation:

#2 x^4 + 5 x^3 y + 45 x y^3 - (34 x^2 y^2 + 18 y^4)=(2 x - 3 y) (x - y)^2 (x + 6 y) = 0#

so solving

#{(x-y=0),(2 x - 3 y=7):}# and

#{(2 x - 3 y=7),(x+6y=0):}#

we get the pairs

#(-7,-7)# and #(14/5,-7/15)#