Question

(05.03 LC)

Determine the solution to f(x) = g(x) using the following system of equations: (5 points)

f(x) = 5.5x − 13
g(x) = −5x + 18.5


x = 1
x = 2
x = 3
x = 4

Answer 1

If g(x) is equal to f(x), then they are the same value.

Put 5.5x - 13 in place of g(x) in the second equation.

5.5x - 13 = -5x + 18.5

Add 13 to both sides.

5.5x = -5x + 31.5

Add 5x to both sides.

10.5x = 31.5

Divide 10.5 on both sides.

x = 3

Hope this helps! :)

Answer 2

The solution to f(x)=g(x) is:

x=3

Explanation:

We are given to functions f(x) and g(x) by:

`f(x)=5.5x-13`

and
`g(x)=-5x+18.5`

Now, we are asked to determine the solution of:

`f(x)=g(x)`

i.e. we are asked to find the possible values of x where the two functions are equal.

i.e.

`5.5x-13=-5x+18.5`

Now , on adding both side of the equality by 5x and 13 we get:

`5.5x+5x=18.5+13\\\\i.e.\\\\10.5x=31.5\\\\\\i.e.\\\\\\x=(31.5)/(10.5)\\\\i.e.\\\\x=3`