Question

What is the positive solution to the system of equations?
[ f(x)=x+4
g(x) = 2x² - 4x + 1

Answer 1

Explanation:

Set both function equal to each other.

`x + 4 = 2 {x}^(2) - 4x + 1`

`0 = 2 {x}^(2) - 5x - 3`

`0 = 2 {x}^(2) - 6x + x - 3`

`0 = 2x(x - 3) + 1(x - 3)`

`0 = (2x + 1)(x - 3)`

`x = - (1)/(2)`

`x = 3`

Let use the positive x value, 3

Plug in either equation to find the y value

`f(3) = 3 + 4 = 7`

So the answer is

(3,7)