How to solve an equation with two variables?

[Bad_at_math]

Hi, I have a very basic question. If you have an equation like the following:

4x + 2y = 20

How would you go about solving it? I've looked online, but the examples I've found aren't exactly what I'm looking for and I'm so bad at math that when I try to adapt the steps they use by changing them slightly for this kind of equation it doesn't seem to work. Obviously for something simple like this you can just plug in numbers until you hit the right combination but I know there's a systematic way to solve it.

Thanks in advance for any help.

 

[Iceycold12]

Hello.

Just to make sure, is it a system of equations? Did they give you two equations? Say:

\(\displaystyle 4x+2y=20\)
and (random choice of numbers just an example)
\(\displaystyle 5x+6y=15\)

Just making sure we have the right equation here.

 

[Bad_at_math]

Hi, no, it's just one equation. I think that's why I'm having trouble using the examples that I'm finding online. They all seem to be systems of equations.

 

[pappus]

Hi, I have a very basic question. If you have an equation like the following:

4x + 2y = 20

How would you go about solving it? ...

If you mean by "solving" that you'll get one single solution then I'm afraid we have to disappoint you.

Your equation describes a straight line which consists of an unlimited number of points. The coordinates of all points located on the line satisfy the given equation. For instance (0, 10), (5, 0), (-1000, -1990) etc.

So if your solution is the set of ordered pairs which satisfy the equation.

 

[wjm11]

4x + 2y = 20

How would you go about solving it?

As pappus has said, you'd need a system of equations to solve for a distinct x and y. In general, you need as many equations as you have variables -- so two equations are needed for two variables.

Perhaps you are asked instead to "solve for y." This does not mean we have to find a specific number value for y. It means simple rearrange the equation so that y is by itself, in the form y = ...

In this case, that would be y = (20 - 4x)/2 (which can then be simplified).

 

[Bad_at_math]

Hi, everyone, thanks for your responses. I guess I'm totally off with this one as I so often am with anything mathematical. Anyway, below is the kind of problem I'm trying to solve.

Bob bought some books that cost $4.00 each. John bought some books that cost $2.00 each. Together they spent $20.00. How many books did Bob buy and how many books did John buy?

To make a long story short, someone posed this question and said there was a formula to figure it out, and that they thought the way to set it up was something like I have in my original post:

4x + 2y = 20

but I guess not. Is there any way to solve this problem with the information given?

Sorry if this is simple. My user name says it all.

 

[pappus]

...

Bob bought some books that cost $4.00 each. John bought some books that cost $2.00 each. Together they spent $20.00. How many books did Bob buy and how many books did John buy?

...

1. Could it be that there is missing some information like "together they bought 7 books"?

2. If not make a table. (see attachment)

 

[Bad_at_math]

Hi, pappus, thanks for your response. Yes, it is possible that there is some missing information. This was something that came up during a discussion about math and algebra and some related topics, not a problem out of an actual textbook. It's been many years since I've taken algebra or any kind of math at all so whenever something like this comes up I never really know how to solve it or if there is even enough information for it to be solved.

Thank you very much for the information and the table idea. That's a very good suggestion.

1. Could it be that there is missing some information like "together they bought 7 books"?

2. If not make a table. (see attachment)