## anonymous one year ago How can 1/5x − 2 = 1/3x + 8 be set up as a system of equations?

1. anonymous

If you say that each equation is equal to some y-value, then you can get a system. I assume you mean 1/5x to be $$\frac{1}{5}x$$ and 1/3x to be $$\frac{1}{3}x$$, correct?

2. anonymous

yes youre correct

3. anonymous

Alright, then let's just say each side of the equality is equal to y. Then we can have this: $$y = \frac{1}{5}x -2$$ $$y=\frac{1}{3}x + 8$$

4. anonymous

okay sounds good

5. anonymous

can you show me whats next

6. anonymous

Well, that's just the set up in order to turn it into a system of equations. Did you need to solve it as well?

7. anonymous

well let me show you the answer choices

8. anonymous

5y-5x=-10 3y-3x=24 5y-5x=-10 3y+3x=24 5y+x=-10 3y+x=24 5y-x=-10 3y-x=24

9. anonymous

Oh, okay, so then we have to turn it into some sort of general form. Well, if we start with $$y = \frac{1}{5}x-2$$, we first want to get rid of the fraction. Do you know how to eliminate fractions in these equations?

10. anonymous

i knnow you would have to multiply

11. anonymous

Yeah. You would multiply by an LCD of any fractions in the equation. Of course the only denominator we have is a 5, so we just multiply everything by 5. Are you comfortable doing that?

12. anonymous

13. anonymous

Well, you see why multiplying everything by 5 is what we need to do, yes?

14. anonymous

yes i do see that

15. anonymous

So if I do this: $$5*y = 5*\frac{1}{5}x - 5*2$$ I get $$5y = x - 10$$ That okay on your end?

16. anonymous

ok.... so which one of my answer choices would that be?

17. anonymous

Well, all of your answer choices have the 5y part as being positive and the number by itself. So that means I want to subtract x from both sides. $$5y = x - 10$$ $$-x -x$$ $$5y - x = -10$$

18. anonymous

okay thank you so much

19. anonymous

You're welcome