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### Course: Algebra (all content)>Unit 2

Lesson 12: Old school equations with Sal

# Linear equations 3

Linear equations with multiple variable and constant terms. Created by Sal Khan.

## Want to join the conversation?

• i dont get the problem at ? can someone please help me i am real stuck thx much
• -5 - 3. Okay. well, there is a way that I know. Remember that subtracting a positive is the same as adding a negative? So that would be the same as saying this:
Lisa owed her dad 5 dollars. When she talked her dad into buying a 3\$ headband he agreed but on the condition that she pay her back. What is her complete debt now?Well, if you add a debt to a debt it is going to make the debt bigger, farther to the LEFT of zero. So consequently that would equal -8.If that doesn't help there is a video called Adding Negative Numbers. He has a really good way of thinking about it!!
• I need to find out linear equations in three variables. So for example, 3x + y - 2z = 10
6x - 2y + z = -2
x + 4y + 3z = 7
Where can i find a answer for questions like this?
• Still do the same substitution or elimination, just multiple times. I prefer elimination.

3x+y-2z=10
6x-2y+z= -2
x+4y+3x=7.

Eliminate a variable of your choice. I will eliminate x. I like to pair the first with the second and then the second with the third.

Multiply first by -2:
-6x-2y+4z= -20
Second: 6x-2y+z= -2
=> -4y+5z= -22.

Multiply third by -6.
-6x-24y-18z= -42
Second: 6x-2y+z= -2
=> -26y-17z= -44.

-4y+5z= -22
-26y-17z= -44
Now let's eliminate y.
Multiply first by -13: 52y-65z=286
Multiply second by 2: -52y-34z= -88
=> -99z=198 => z= -2 => y=3 => x=1.
=> (1,3,-2).
It's been a long time since I learned this, but I think that it's later on in Algebra 1.
• i need help on a problem like... 6(3x-5)-7x=25
• 6(3x-5)-7x=25
18x-30-7x=25
11x-30=25
11x=55
x=5
• why is it called linear equations
• When you graph a linear equations, the graph will be a straight line. Linear means "line". This is why they are called linear equations.
• So basically you just reduce a level 3 problem to a two, and a level two problem to a level one problem, and then you get the answer?
• Yes! Essentially that's all problem-solving is. You take a hard problem, and you make it a bit easier, then you keep making it a bit easier until it's easy enough that you can solve it.
• in I got 11/-3. Is it the same as -11/3?
• Yes it is.
(1 vote)
• sorry for disturbing you, but on the second question, there was -2x at the first step so after doing the first step why does sir make it into -3x ?
• Sal subtracted "x" from both sides to move the "x" on the right side over to the left side. When combined with the "-2x" on the left side, you get "-3x".
-x-2x = -3x

Hope this helps.
• dang thats crazy i learned how to do math i think im smort
• Thank you man but I got a question. if you cancel out 1 side first you get different answers.
Lets say the equation 2x+3=-15
We could do this
2x+3+15=-15+15
2x=18
x=9
or this
2x+3-3=-15-3
2x=-18
x=-9
• You have an error in your first calculation.
2x+3+15=-15+15 becomes 2x+18=0
You are moving the 15 to the left side of the equals. So, the right side becomes 0. This does not help you solve the equation - it just gives you extra work steps. You should always focus on the location of the variable (the left side in this equation) and move numbers away from that side.

Hope this helps.