Answer
$$\left\{ {\left( { - 1,1} \right),\left( { - \frac{3}{5},\frac{7}{5}} \right)} \right\}$$
Work Step by Step
$$\eqalign{
& 3{x^2} + 2{y^2} = 5\,\,\,\,\,\,\,\left( {\bf{1}} \right) \cr
& \,\,\,\,\,\,\,\,\,x - y = - 2\,\,\,\,\left( {\bf{2}} \right) \cr
& \cr
& {\text{Solve the equation }}\left( {\bf{2}} \right){\text{ for }}y \cr
& y = x + 2 \cr
& {\text{Substitute }}x + 2{\text{ for }}y{\text{ into the equation }}\left( {\bf{1}} \right) \cr
& 3{x^2} + 2{\left( {x + 2} \right)^2} = 5 \cr
& 3{x^2} + 2\left( {{x^2} + 4x + 4} \right) = 5 \cr
& 3{x^2} + 2{x^2} + 8x + 8 = 5 \cr
& 5{x^2} + 8x + 3 = 0 \cr
& {\text{Solve for }}x \cr
& \left( {5x + 3} \right)\left( {x + 1} \right) = 0 \cr
& {x_1} = - \frac{3}{5},\,\,\,\,{x_2} = - 1 \cr
& \cr
& {\text{Substitute }}{x_1} = - \frac{3}{5}{\text{ into the equation }}y = x + 2{\text{ to find }}\left( {{x_1},{y_1}} \right) \cr
& y = - \frac{3}{5} + 2 \cr
& y = \frac{7}{5} \cr
& {\text{The first solution is }}\left( { - \frac{3}{5},\frac{7}{5}} \right) \cr
& \cr
& {\text{Substitute }}{x_2} = - 1{\text{ into the equation }}y = x + 2{\text{ to find }}\left( {{x_2},{y_2}} \right) \cr
& y = - 1 + 2 \cr
& y = 1 \cr
& {\text{The second solution is }}\left( { - 1,1} \right) \cr
& \cr
& {\text{Therefore, the solution set of the system is}} \cr
& \left\{ {\left( { - 1,1} \right),\left( { - \frac{3}{5},\frac{7}{5}} \right)} \right\} \cr} $$
