10.3. Plot on the coordinate plane the set of points satisfying the equation $2 x^{2}+y^{2}+3 x y+3 x+y=2$.

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The sought set of points is the union of two lines $y=-x-2$ and $y=-2x+1$. Solution. Consider the given equation as a quadratic equation in terms of $y: y^{2}+y(3x+1)+2x^{2}+3x-2=0$. Its discriminant is $D=x^{2}-6x+9=(x-3)^{2}$, and the solutions are $y_{1}=-x-2, y_{2}=-2x+1$. These solutions represent two lines on the coordinate plane.