Question

Does someone mind helping me with this? Thank you!

Answer 1

(1, - 8) and (2, -9)

Explanation:

We have the following system of equations

`\begin {aligned}\\f(x) & = x^2 - 4x - 5\\f(x) & = -x - 7\\\end{aligned}`

Setting the right side of each of these expressions equal to each other gives us:

`x^2 - 4x - 5 = -x - 7\\`

Add x to both sides:

`x^2 - 4x + x - 5 = -x + x - 7\\\\x^2 -3x -5 = -7\\`

Add 7 to both sides:

`x^2 - 3x - 5 + 7 = -7 + 7\\x^2 - 3x + 2 = 0\\`

This is a quadratic equation which can be easily solved by factoring:

`x^2 - 3x + 2 = 0 \\\\ (x - 1) (x - 2) = 0\\\\\implies x- 1 = 0 or x - 2= 0\\x - 1 = 0 = > x = 1\\x - 2 = 0 = > x = 2\\`

So the possible solutions are x = 1 and x = 2

Substituting each of these values for x in the second equation(or the first) will yield the value of f(x) for that value of x

At x = - 1, -x - 7 ==> -1 - 7 = -8
So one ordered pair is (1, -8)

At x = 2, -x - 7 ==>-2 - 7 = -9
So the other ordered pair is (-2, -9)