Four equations? Maybe.Originally Posted byDenMac21

But here is one way.

Just by looking, [x=2 and y=3] or [x = -2 and y = -3] or [x=3, y=2] or [x= -3, y= -2] are the answers. Four sets of them.

By computations, let us see.

|x +y| = 5 means [x+y = 5] or [x+y = -5]

|xy| = 6 means [xy = 6] or [xy = -6]

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When x+y = 5, and xy = 6:

From the 2nd equation, y = 6/x

So, in the 1st equation,

x +6/x = 5

x^2 +6 = 5x

x^2 -5x +6 = 0

(x-2)(x-3) = 0

x = 2 or 3

And so, y = 6/2 or 6/3 = 3 or 2

Meaning, [x=2, y=3] or [x=3, y=2] ----------answer.

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When x+y = -5, and xy = 6:

From the 2nd equation, y = 6/x

So, in the 1st equation,

x +6/x = -5

x^2 +6 = -5x

x^2 +5x +6 = 0

(x+2)(x+3) = 0

x = -2 or -3

And so, y = 6/(-2) or 6/(-3) = -3 or -2

Meaning, [x= -2, y= -3] or [x= -3, y= -2] ----------answer.

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When x+y = 5, and xy = -6:

From the 2nd equation, y = -6/x

So, in the 1st equation,

x -6/x = 5

x^2 -6 = 5x

x^2 -5x -6 = 0

(x-6)(x+1) = 0

x = 6 or -1

And so, y = -6/6 or -6/(-1) = -1 or 6

Meaning, [x=6, y= -1] or [x= -1, y=6] ----------answer.

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When x+y = -5, and xy = -6:

From the 2nd equation, y = -6/x

So, in the 1st equation,

x -6/x = -5

x^2 -6 = -5x

x^2 +5x -6 = 0

(x+6)(x-1) = 0

x = -6 or 1

And so, y = -6/(-6) or -6/1 = 1 or -6

Meaning, [x= -6, y=1] or [x=1, y= -6] ----------answer.