Question

Y=x​2​​−6x+10​
y=4−x​​


How do I substitute?

Answer 1

(2,2) and (3,1)

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)