Y=x^2-6x+9
x+y=5
Substitution

{1, 4}

Step-by-step explanation:

Solve the second equation for y in terms of x:  x + y = 5  =>  y = 5 - x

Substituting this expression for y into the first equation, we obtain:

5 - x = x^2 - 6x + 9

Subtracting 5 from both sides yields

-x = x^2 - 6x + 4

Then, adding x to both sides yields

0 = x^2 - 5x + 4, which factors as follows:

0 = (x - 4)(x - 1)

Setting each factor equal to 0 separately and solving for x in each case results in the solutions {1, 4}