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is 2x+x=2x or does it equal3x

solve the system is the question th system is x+5y=17 and the other equation is 2x+3y=13 so you put them n top and add them together my question is when you add 2x+x would it be 2x or 3x or 2x^2



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4 Answers

Just remember when there is no number or coefficient before a variable it is understood to be 1.   So 2x + x is actually 2x + 1x which equals 3x.  If you have trouble remembering that I just suggest anytime you see a variable without a coefficient write in a "1" where the coefficient would be.

When you are adding and subtracting equations, you add and subtract them just like you add and subtract numbers. Also, it sounds like you are trying to find the solution to a system of linear equations using elimination. If you are going to use this method, you need to eliminate one of the variables to solve for the other.

So, if you wanted to add the equations, you can multiply the first equation by -2, which would give you -2x - 10y = -34. Now, compare the two equations:

-2x - 10y = -34

2x + 3y = 13

If you notice, I have decided to elimnate x (remember, you can start by eliminating y if you want) If I add the equations, then the terms containing x vanish and I have

-7y = -21

Now, you can see that there is one unknown left and dividing through by -7 gives y = 3. 

I would have one of my own students, when encountering this problem, take a few minutes to write things like "2x + 3x = 5x, 4x - x = 3x, etc." and then have them do "x * 3x = 3x^2".  You know, pick 20 or so random things to write where you're first adding, then multiplying.

It seems like busy work, but because the idea is confusing if you think it through, it's worth it to spend 10 minutes or so just training your brain to do it.  Next time you ask this question, think it through once, spend 10 minutes drilling the correct answer to your question, and you'll probably never stumble over this again.

That's a page I took from martial art training, actually, where the idea is to train your muscles to know how to make the moves so you don't have to think through them.  Same idea here, just different moves.

When adding like numbers you just add. So 2x+x would equal 3x. You would get 2x^2 is you multipied 2x and x together.


I hope this helps.