# Solve simultaneously for x and y in the following system of equations: x+ y = 3 and 2x^2 + 2y^2 = 5xy

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### 1 Answer

`x+y = 3`

`y = 3-x`

`2x^2 + 2y^2 = 5xy`

`2x^2+2(3-x)^2 = 5x(3-x)`

`2x^2+2(x^2-6x+9) = -5x^2+15x`

`2x^2+2x^2-12x+18 = -5x^2+15x`

`4x^2-12x+18 = -5x^2+15x`

`9x^2-27x+18 = 0`

`x^2-3x+2 = 0`

`x^2-2x-x+2 = 0`

`x(x-2)-1(x-2) = 0`

`(x-2)(x-1) = 0`

`x = 1 ` and `x = 2`

When x = 1 then y = 3-1 = 2

When x = 2 then y = 3-2 = 1

*So the answer pairs are (1,2) and (2,1)*