It is known that x = 1, y = 1 and x = 2, y = - 3 are the solutions of the quadratic equation with respect to X and y, then the equation is:

It is known that x = 1, y = 1 and x = 2, y = - 3 are the solutions of the quadratic equation with respect to X and y, then the equation is:

Any quadratic equation of two variables can be written as: x + by + C = 0
(Note: there is no a because if there is a, it can also be removed.)
The rest is to solve the equations
Take x = 1, y = 1 and x = 2, y = - 3 and find B and C
The solution is: B = 1 / 4, C = - 5 / 4
So the equation is: x + 1 / 4 * y - 5 / 4 = 0
A good point is: 4x + y = 5