X+y=-11 xy=-12

To solve this system of equations with two variables, we can use substitution or elimination method. Let's solve it using the substitution method.

From the first equation, we have: x = -11 - y

Now we substitute this value of x in the second equation: (-11 - y)y = -12

Expanding and simplifying the equation: -11y - y^2 = -12

Moving all terms to one side: y^2 + 11y - 12 = 0

Now we can factor or use the quadratic formula to solve for y. Factorizing this equation: (y + 12)(y - 1) = 0

Setting each factor to zero: y + 12 = 0 or y - 1 = 0

y = -12 or y = 1

Now substitute the values of y back into the first equation to find the corresponding values of x.

For y = -12: x + (-12) = -11 x - 12 = -11 x = -11 + 12 x = 1

For y = 1: x + 1 = -11 x = -11 - 1 x = -12

Therefore, the solutions to the system of equations are (x, y) = (1, -12) and (x, y) = (-12, 1).