Using System of Equations for Sums and Differences of Functions

[Cosmos]

I'm stumped on a question that I'm sure I need to use the System of Equations to solve:

If f(x) + g(x) = 5x-2

and if f(x) - g(x) = x + 2...

Find f(x) and g(x).


Problem is, I don't know where to start. I tried substituting f(x) and g(x) with variables and then solving for each variable (I'm sure this is wrong as I ended up with a numerical value). I thought that for System of Equations, you have to solve for one variable in the first equation, then substitute this into the second equation to find the value of the other variable, and then so on and so forth. How do I start this thing?

Thanks.

 

[MarkFL]

Hint: try adding the two equations to eliminate \(\displaystyle g(x)\)...

 

[Cosmos]

Hint: try adding the two equations to eliminate \(\displaystyle g(x)\)...

Ah, ok thanks. So I get f(x) = 6x and solving g(x) in the first equation, I get -x - 2. Why doesn't the second equation equal x + 2 when I plug in the values?

Sorry for the questions, we didn't cover this material in school.

 

[MarkFL]

Hey, forums are for posting questions and discussing things, so no need to apologize.

Now, when you add the equations, you should get:

\(\displaystyle 2f(x)=6x\)

Now, we need to divide through by 2 to solve for \(\displaystyle f(x)\):

\(\displaystyle f(x)=3x\)

Now, substitute for \(\displaystyle f(x)\) into either of the original equations to find \(\displaystyle g(x)\).

 

[Cosmos]

Hey, forums are for posting questions and discussing things, so no need to apologize.

Now, when you add the equations, you should get:

\(\displaystyle 2f(x)=6x\)

Now, we need to divide through by 2 to solve for \(\displaystyle f(x)\):

\(\displaystyle f(x)=3x\)

Now, substitute for \(\displaystyle f(x)\) into either of the original equations to find \(\displaystyle g(x)\).

Thanks MarkFL, you saved my life!! Ok not really, but I'm sure I'll get this question right on the exam today!