Solve the simultaneous equation
x²+xy+2y²=4
2x+3y=-1

Use substitution 
from the second equation  y =  (-1-2x) / 3. Plug this into the first equation:-
x^2 + x(-1-2x)  + 2(-1-2x)^2  =  4
                 
              3                 9

multiply through by 9:-

9x^2 + 3x(-1 - 2x) + 2(-1-2x)^2 = 36
9x^2 - 3x - 6x^2 + 2(1 + 4x + 4x^2) = 36
9x^2 - 3x - 6x^2 + 2 +8x + 8x^2 = 36
11x^2 +5x -34 = 0
which you can solve using the quadratic formula
   Then substitute the 2 values of x into the second equation to find values of y.           

Chope that

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