Question

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`?

Answer 1

`(-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)`