#### Question

Solve the system of two quadratic equations with two variables

Collected in the board: System of equations

Steven Zheng posted 5 months ago

Observe the equations and add 2\times ( 1)+(2)

(x+y)^2+2(x+y)-3=0

Factoring the LHS

(x+y-3)(x+y+1) = 0

Then, we get

x+y-3=0 \text{ or } x+y+1=0

Substituting them to (1) gives two system of equations

\begin{cases} x+y-3=0 \\xy = -10 \end{cases}
(3)

\begin{cases} x+y+1=0 \\xy=14 \end{cases}
(4)

Solving (3) obtains