Question

Y=x​2​​−6x+10​ y=4−x​​ How do I substitute?

Answer 1

Answer:

(2,2) and (3,1)

Step-by-step explanation:

Since we're given the value of y in the second equation, we can replace the y on the left side of the first equation with 4-x, giving us

$4-x=x^2-6x+10\\0=x^2-5x+6$

We can factor the expression on the right to get us

$0=x^2-5x+6\\0=x^2-3x-2x+6\\0=x(x-3)-2(x-3)\\0=(x-2)(x-3)$

Solving $x-2=0$ and $x-3=0$ gets us the solutions $x=2,3$, which we can plug into the second equation to get us

$y=4-2=2\\y=4-3=1$

So, our solution set is the pair of points (2,2) and (3,1)