MATH SOLVE

3 months ago

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

Accepted Solution

A:

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)