Question

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

Answer 1

The solution of the given system is (2,0)

Explanation:

Here, the given system of equations is:

x + y = 2 .............. (1)

`y= x^2 - 6x +  8` ........ (2)

Now from (1) x = 2 - y

Substitute this value of x = 2- y in (2) ,we get:

`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`

⇒ y = 0 or, y = -1

Now, if y = 0, x = 2

and if x= -1, y = 2-(-1) = 2+1 = 3, or y = 3

But (x = -1 , y = 3 )is NOT a solution of (2).

Hence, the solution of the given system is (2,0)