Mister Exam
2x+2y+xy=8; x^2+y^2+3x+3y=14
The solution
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2*x + 2*y + x*y = 8
$$x y + \left(2 x + 2 y\right) = 8$$
2 2 x + y + 3*x + 3*y = 14
$$3 y + \left(3 x + \left(x^{2} + y^{2}\right)\right) = 14$$
3*y + 3*x + x^2 + y^2 = 14
Rapid solution
$$x_{1} = 1$$
=
$$1$$
=
$$y_{1} = 2$$
=
$$2$$
=
=
$$1$$
=
1
$$y_{1} = 2$$
=
$$2$$
=
2
$$x_{2} = 2$$
=
$$2$$
=
$$y_{2} = 1$$
=
$$1$$
=
=
$$2$$
=
2
$$y_{2} = 1$$
=
$$1$$
=
1
$$x_{3} = - \frac{5}{2} - \frac{5 \left(-5 - \sqrt{3} i\right)^{2}}{12} - \frac{5 \sqrt{3} i}{6} - \frac{\left(-5 - \sqrt{3} i\right)^{3}}{12}$$
=
$$-5 + \sqrt{3} i$$
=
$$y_{3} = -5 - \sqrt{3} i$$
=
$$-5 - \sqrt{3} i$$
=
=
$$-5 + \sqrt{3} i$$
=
-5 + 1.73205080756888*i
$$y_{3} = -5 - \sqrt{3} i$$
=
$$-5 - \sqrt{3} i$$
=
-5 - 1.73205080756888*i
$$x_{4} = - \frac{5}{2} - \frac{\left(-5 + \sqrt{3} i\right)^{3}}{12} + \frac{5 \sqrt{3} i}{6} - \frac{5 \left(-5 + \sqrt{3} i\right)^{2}}{12}$$
=
$$-5 - \sqrt{3} i$$
=
$$y_{4} = -5 + \sqrt{3} i$$
=
$$-5 + \sqrt{3} i$$
=
=
$$-5 - \sqrt{3} i$$
=
-5 - 1.73205080756888*i
$$y_{4} = -5 + \sqrt{3} i$$
=
$$-5 + \sqrt{3} i$$
=
-5 + 1.73205080756888*i