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### Course: 6th grade (WNCP) > Unit 2

Lesson 2: Variables and equations- Expressions with two variables
- Writing expressions with variables
- Writing basic expressions word problems
- Evaluating expressions with one variable
- Evaluating expressions with multiple variables
- Evaluating expressions with variables word problems
- Combining like terms
- Combining like terms with negative coefficients
- Combining like terms with negative coefficients
- Equivalent expressions
- Model with one-step equations
- One-step multiplication & division equations
- One-step addition & subtraction equations

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# Expressions with two variables

Basics of expression with two variables. Created by Sal Khan.

## Want to join the conversation?

- I'm confused, wouldn't -10 - 15 equal positive 5 not negative 25? If it were to equal a negative wouldnt the equation have looked like this instead instead of how it was shown. -10 - -15? And if it were to look like this then wouldnt the two minuses in the middle make a plus, and if this be the case then would it equal positive 25 not negative 1?(77 votes)
- Think of it as a bank account. You spent $10 more than you have so you have $-10. Then you go buy new shoes for $15 so you owe the bank $25.(7 votes)

- Why 10(-1) is -10 and not 1/10?(0 votes)
- You are multiplying not dividing.(10 votes)

- what if theirs a fraction that's where I tend to get confused the most(3 votes)
- if I want to learn how to do algebra 1 what should I look up(2 votes)
- The algebra 1 track starts here: https://www.khanacademy.org/math/algebra

If that is too difficult, start here: https://www.khanacademy.org/math/algebra-basics

And if even that is too difficult, start here: https://www.khanacademy.org/math/pre-algebra(3 votes)

- How do I solve these systems 2x + 4y =5

3x- 2y =10(1 vote)- Let's say equation 1 is 2x + 4y = 5 and equation 2 is 3x - 2y = 10

If we multiply all of equation 2 by a factor of 2 we get 2*(3x - 2y) = 2*10 which is 6x - 4y = 20 (let's call this equation 3). Now we will add equation 1 and equation 3 which is 2x + 4y + (6x - 4y) = 5 + 20, simplify and we get 8x = 25. The important thing to take away here is that we got rid of the y term because we have +4y and -4y which equals 0y so y's disappear. We get 8x = 25 which means x = 25/8, now we can use equation 1 (or 2) and sub in 25/8 for x and solve for y. So 2*(25/8) + 4y = 5 and this equals 50/8 + 4y = 5 and y = -5/16(5 votes)

- Why would the answer be -25? Wouldn't it be -5?(2 votes)
- You can find out why it is -25 here: https://www.khanacademy.org/math/arithmetic/absolute-value(2 votes)

- im very confused with the equation below because i need more explanation to it(2 votes)
- Hmm... This is only useful if you are given the answer to one or both of the equations already. I remember learning how to resolve a 2-variable system with 2 equations, with no possible solutions already given, but I can't at all remember how to go about doing it.

IIRC, you had to isolate one of the variables? And then replace it with its equal in the other equation? Buuuut I'm getting weird results; I keep getting 0x or 0y? Not sure what went wrong there.

Say I have a system of "14x-2y=40" and "y=7x-8". I replace the y= in the first equation, getting 14x-2(7x-8)=40... I end up with 14x-14x=24, which seems impossible. Am I making a huge mistake, or is the thing rigged? >_>

Edit: It was rigged! Googled stuff, found another method (the elimination method), which helped prove that this one doesn't have a solution. Well, it's nice to know that I still remember how to do some things. :)(2 votes) - At1:33, Sal is doing 10(-1) -3(5). He did 10 times -1, is the next step 3 x 5 and when you rewrite the problem (-10)-(15) or is it -3 x 5? I know they end up with the same answer but I want to know what they do what to do, like which step is correct if they both have different answer.(2 votes)
- So I'm in a class for CNC machining and the math problems are like this

10x+15=3x-17 there's nothing that say's what x is can you help me on this issue(1 vote)

- Can you make a video on a million pi? Or is that already there?(2 votes)

## Video transcript

Now, let's think about expressions with more than one variable. So, let's say I had the expression "a + b" and I were to ask you what is this expression equal to when "a" is equal to 5 and "b" is equal to 7 Well, in this situation, this expression would be... instead of an "a" we would have a 5 it would be 5 plus... instead of a "b", we would have a 7. So it would be 5 + 7 is equal to 12. Now let's try another expression. Let's say we had the expression "10x - 3y" And, let's think about what would this expression evaluate to when "x" is equal to - 1 and when "y" is equal to 5. Well, let's just evaluate it. We have 10 times... instead of an "x", we know now that "x" is equal to -1, it would be 10 (-1) - 3 (5). So three times... instead of a "y", we will put a 5 there. - 3 (5). And so 10 (-1), that is -10 and we're going to subtract from that 3 (5). You want to do the multiplication first by order of operations that's the convention. 3 times 5 is 15. So, it is -10 - 15, which is equal to -25. And now, you have the next exercise to practice some of these a little bit more.