Solving Systems by Graphing

[lovehopefaith98]

I am having trouble with a word problem that was on a worksheet for solving systems using graphing. Here is the problem:

Five years from now, a father's age will be three times his son's age, and 5 years ago, he was seven times as old as his son was. What are their present ages?

I don't think I am doing this right, but this is what I did:
y=3x + 5
y=7x - 5

I then graphed the equations, and got the solution as (1,2). From here, I am stuck.

Thanks for the help!

 

[soroban]

Hello, lovehopefaith98!

Your set-up is incorrect.

Five years from now, a father's age will be three times his son's age.
Five years ago, he was seven times as old as his son was.
What are their present ages?

Let \(\displaystyle x\) = son's present age.
Let \(\displaystyle y\) = father's present age.

Five years from now, they both will be 5 years older.
The son will be \(\displaystyle x+5\) years old.
The father will be \(\displaystyle y + 5\) years old.
In the future: .\(\displaystyle y+5 \:=\:3(x+5) \quad\Rightarrow\quad \boxed{y \:=\:3x+10}\)

Five years ago, they both were 5 years younger.
The son was \(\displaystyle x-5\) years old.
The father was \(\displaystyle y-5\) years old.
Back then: .\(\displaystyle y-5 \:=\:7(x-5) \quad\Rightarrow\quad \boxed{y \:=\:7x-30}\)

Now graph those two line . . .

 

[lovehopefaith98]

Thanks to both of you for your help! It is really appreciated.
So, is the answer 10 years old for the son and 40 years old for the father?

 

[wjm11]

So, is the answer 10 years old for the son and 40 years old for the father?

You can always check your answers easily by plugging them back into BOTH equations and verifying that they work.