Solve the system

x+y+\dfrac{1}{x}+\dfrac{1}{y} = \dfrac{9}{2} \\ xy+\dfrac{1}{xy} =\dfrac{5}{2}

Solve the system

x^2+xy+y^2=19 \\ x^2+y^2+x+y=18

If 2x^2+3xy-2y^2-5(2x-y)=0 and x^2-2xy-3y^2+15=0

Find the value of x,y

Solve the system

xy=-64 \\\dfrac{1}{x}-\dfrac{1}{y}=\dfrac{1}{4}

Solve the system equations

x+xy+y=11\\x^2y+xy^2=30

If x^2+xy+y^2=39, y^2+yz+z^2=49, z^2+zx+x^2=19, find all soltion sets for of x, y , z

Solve the system of quadratic equations with three variables

\begin{cases} xy+x+y=-13 \qquad\quad\,\, (1) \\ yz+y+z = -9 \qquad\qquad (2)\\ zx+z+x = 5 \qquad\qquad\,\,\,\, (3)\end{cases}

Solve the system of two quadratic equations with two variables

\begin{cases} xy+x+y=-13 \qquad\qquad (1)\\x^2+y^2 = 29 \qquad\qquad\qquad\: (2)\end{cases}