Solve the system by the substitution method.x + y = 2y= x2 - 6x + 8

Answer:The solution of the given system is (2,0)Step-by-step explanation:Here, the given system of equations is:x + y = 2    .............. (1)[tex]y= x^2 - 6x +  8[/tex]  ........  (2)Now from (1) x = 2 - ySubstitute this value of x = 2- y in (2) ,we get:[tex]y= (2-y)^2 - 6(2-y) +  8\\\implies y = 4 + y^2 - 4y - 12 + 6y + 8\\or, y^2 + y  = 0\\\implies y(y +1) = 0[/tex]⇒  y = 0 or,  y = -1Now, if y = 0, x  = 2and if x= -1, y = 2-(-1)  = 2+1  = 3, or y = 3But (x = -1 , y = 3 )is NOT  a solution of (2).Hence, the solution of the given system is (2,0)