Consider the system of equationsx + y z = 1,x + y + z = 1,x+y+z = 1.Determine all solutions in C3 using the Elimination

Consider the system of equationsx³ + y³ z³ = 1,x² + y² + z² = 1,x+y+z = 1.Determine all solutions in C3 using the Elimination and the Extensions Theorems. You are allowed to use computer algebra software besides the commands that solve a system of polynomial equations directly. Explain your work.