Question

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

Answer 1

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?

Answer 2

yes youre correct

Answer 3

Alright, then let's just say each side of the equality is equal to y. Then we can have this:

\(y = \frac{1}{5}x -2\)
\(y=\frac{1}{3}x + 8\)

Answer 4

okay sounds good

Answer 5

can you show me whats next

Answer 6

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?

Answer 7

well let me show you the answer choices

Answer 8

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

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

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

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

Answer 9

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?

Answer 10

i knnow you would have to multiply

Answer 11

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?

Answer 12

can you please do it for me. i already tried

Answer 13

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

Answer 14

yes i do see that

Answer 15

So if I do this:
\(5*y = 5*\frac{1}{5}x - 5*2\) I get

\(5y = x - 10\)

That okay on your end?

Answer 16

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

Answer 17

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.
\(5y = x - 10\)
\(-x -x\)

\(5y - x = -10\)

Answer 18

okay thank you so much

Answer 19

You're welcome