Log in Dwight Crowell 10 years agoPosted 10 years ago. Direct link to Dwight Crowell's post “Why is it that when the e...” Why is it that when the equation works out to be 13=13, 5=5 (or anything else in that pattern) we say that there is an infinite number of solutions? • (28 votes) TuckerS a year agoPosted a year ago. Direct link to TuckerS's post “13=13 Is a true statement...” 13=13 Is a true statement...that is why. (7 votes) Lysandre Ishvar 4 years agoPosted 4 years ago. Direct link to Lysandre Ishvar's post “Does the same logic work ...” Does the same logic work for two variable equations? Is there any video which explains how to find the amount of solutions to two variable equations? Help would be much appreciated and I wish everyone a great day! • (12 votes) Ian Pulizzotto 4 years agoPosted 4 years ago. Direct link to Ian Pulizzotto's post “For a system of two linea...” For a system of two linear equations and two variables, there can be no solution, exactly one solution, or infinitely many solutions (just like for one linear equation in one variable). If the two equations are in standard form (both variables on one side and a constant on the other side), then the following are true: 1) lf the ratio of the coefficients on the x’s is unequal to the ratio of the coefficients on the y’s (in the same order), then there is exactly one solution. 2) lf the coefficients ratios mentioned in 1) are equal, but the ratio of the constant terms is unequal to the coefficient ratios, then there is no solution. 3) lf the coefficient ratios mentioned in 1) and the ratio of the constant terms are all equal, then there are infinitely many solutions. (13 votes) zkcookie57 10 months agoPosted 10 months ago. Direct link to zkcookie57's post “At 3:09, in the first exa...” At (4 votes) RainbowSprinkles🏳️🌈 10 months agoPosted 10 months ago. Direct link to RainbowSprinkles🏳️🌈's post “Don’t worry, you didn’t m...” Don’t worry, you didn’t miss anything. :) (23 votes) evanjisaacs a year agoPosted a year ago. Direct link to evanjisaacs's post “You know, Math makes no s...” You know, Math makes no sense, you can literally end up with answers like this: 8=3. or something confusing like that. So why does this work? • (6 votes) AD Baker a year agoPosted a year ago. Direct link to AD Baker's post “If you have ended with an...” If you have ended with an expression like 8 = 3, there is an error in your solution or, if you are working with a system of equations, then there is no solution that satisfies all the equations in the system. 8 = 3 is not an answer. It either means that you need to review your work or that there is no answer. (9 votes) 22mercb 2 years agoPosted 2 years ago. Direct link to 22mercb's post “I don't know if its dumb ...” I don't know if its dumb to ask this, but is sal a teacher? • (4 votes) 𝐢ᴀɴᴅʏ_Qɪ 2 years agoPosted 2 years ago. Direct link to 𝐢ᴀɴᴅʏ_Qɪ's post “Sorry, repost as I posted...” Sorry, repost as I posted my first answer in the wrong box. According to a Wikipedia page about him, Sal is: "[a]n American educator and the founder of Khan Academy, a free online education platform and an organization with which he has produced over 6,500 video lessons teaching a wide spectrum of academic subjects, originally focusing on mathematics and sciences." So technically, he is a teacher, but maybe not a conventional classroom one. Hope that helped! (9 votes) Vio 9 months agoPosted 9 months ago. Direct link to Vio's post “Can -7x+3=2x+2-9x equal t...” Can -7x+3=2x+2-9x equal to 1=0? • (4 votes) Kim Seidel 9 months agoPosted 9 months ago. Direct link to Kim Seidel's post “Your work is correct so f...” Your work is correct so far, but incomplete. (8 votes) Speed 3 months agoPosted 3 months ago. Direct link to Speed's post “hey uh, can people fly?” hey uh, can people fly? • (3 votes) FreeRadical 3 months agoPosted 3 months ago. Direct link to FreeRadical's post “If you throw them hard en...” If you throw them hard enough... (10 votes) Moises 10 months agoPosted 10 months ago. Direct link to Moises's post “so when 0=0, its always i...” so when 0=0, its always infinite solutions ? • (4 votes) Kim Seidel 10 months agoPosted 10 months ago. Direct link to Kim Seidel's post “Yes, and you could even h...” Yes, and you could even have 5=5 of -8=-8. If the variable has been eliminated and you have a number = itself, the equation is an identity (always true). You can use any value for the variable and the two sides of the equation will be equal. (8 votes) Remedy 8 months agoPosted 8 months ago. Direct link to Remedy's post “Though I might have been ...” Though I might have been overlooking something... I have a question about the second scenario, -7x+3=2x+2-9x. Sal adds 7x to the both sides first, but is this acceptable to add/subtract constants (idk how should I call these numbers) first? The result is 0=-1 in this case and there are also no solutions, still I want to make it clear whether there is an order of calculation or not. • (3 votes) Just a girl who loves Jesus 8 months agoPosted 8 months ago. Direct link to Just a girl who loves Jesus's post “I was kind of wondering t...” I was kind of wondering the same thing. Me and my sister have found Khan Acadamy's math courses rather confusing, while their videos normally make sense, a lot of their exercises are really confusing. (9 votes) Joshua Kim 9 years agoPosted 9 years ago. Direct link to Joshua Kim's post “What if you replaced the ...” What if you replaced the equal sign with a greater than sign, what would it look like? Would it be an infinite solution or stay as no solution • (2 votes) DY 9 years agoPosted 9 years ago. Direct link to DY 's post “Like systems of equations...” Like systems of equations, system of inequalities can have zero, one, or infinite solutions. If the set of solutions includes any shaded area, then there are indeed an infinite number of solutions. (8 votes)Want to join the conversation?
3:09
Let’s review the idea of ”number of solutions to equations” real quick. Basically, an equation can have:
Exactly one solution, like 2x = 6. It solves as x = 3, no other options.
No solutions, like x+6 = x+9. This would simplify to 6 = 9, which is, ummm, not true, so no solutions.
Infinitely many solutions, such as 3x = 3x. This simplifies to x = x.
So there’s the part you’re likely confused about. Why does x = x mean infinitely many solutions? Well, because… anything is equal to itself (duh) so literally any number could be an answer. Solve x as 473? 473 = 473, yup! And 64 = 64, and -1.24 = -1.24.
Sal takes away both X’s that’s what you do when solving an equation, you do the same thing to both sides. So x = x becomes just an equal sign!
Essentially, if you can simplify an equation down to just an equals sign, it has infinitely many solutions.
I hope this helped! :D
-7x+3=2x-9x+2
-7x+3-2=-7x
Then I am pretty sure the -7x's cancel out so:
1=0
Is this still correct?
1=0 is a false statement (a contradiction). It is trying to tell you that the equation has no solution. You need to make that interpretation to say that the equation has no solution.
Video transcript
Determine thenumber of solutions for each of theseequations, and they give us three equations right over here. And before I deal with theseequations in particular, let's just remindourselves about when we might have one orinfinite or no solutions. You're going tohave one solution if you can, bysolving the equation, come up with something likex is equal to some number. Let's say x isequal to-- if I want to say the abstract--x is equal to a. Or if we actuallywere to solve it, we'd get something like xequals 5 or 10 or negative pi-- whatever it might be. But if you could actuallysolve for a specific x, then you have one solution. So this is one solution,just like that. Now if you go and you try tomanipulate these equations in completely legitimateways, but you end up with something crazylike 3 equals 5, then you have no solutions. And if you just thinkabout it reasonably, all of these equationsare about finding an x that satisfies this. And if you were to justkeep simplifying it, and you were to getsomething like 3 equals 5, and you were to askyourself the question is there any x that can somehowmagically make 3 equal 5, no. No x can magicallymake 3 equal 5, so there's no way that you couldmake this thing be actually true, no matterwhich x you pick. So if you get somethingvery strange like this, this means there's no solution. On the other hand, if you getsomething like 5 equals 5-- and I'm just overusing the number 5. It didn't have tobe the number 5. It could be 7 or 10or 113, whatever. And actually letme just not use 5, just to make sure that youdon't think it's only for 5. If I just get something,that something is equal to itself,which is just going to be true no matter whatx you pick, any x you pick, this would be true for. Well, then you havean infinite solutions. So with that as alittle bit of a primer, let's try to tacklethese three equations. So over here, let's see. Maybe we could subtract. If we want to get rid of this2 here on the left hand side, we could subtract2 from both sides. If we subtract 2from both sides, we are going to be leftwith-- on the left hand side we're going to beleft with negative 7x. And on the righthand side, you're going to be left with 2x. This is going tocancel minus 9x. 2x minus 9x, If we simplifythat, that's negative 7x. You get negative 7x isequal to negative 7x. And you probably seewhere this is going. This is already truefor any x that you pick. Negative 7 times that x is goingto be equal to negative 7 times that x. So we already are goinginto this scenario. But you're like hey, soI don't see 13 equals 13. Well, what if you didsomething like you divide both sides by negative 7. At this point, what I'mdoing is kind of unnecessary. You already understand thatnegative 7 times some number is always going to benegative 7 times that number. But if we were to do this,we would get x is equal to x, and then we could subtractx from both sides. And then you wouldget zero equals zero, which is true forany x that you pick. Zero is always goingto be equal to zero. So any of thesestatements are going to be true for any x you pick. So for this equationright over here, we have an infinitenumber of solutions. Let's think about this oneright over here in the middle. So once again, let's try it. I'll do it a littlebit different. I'll add this 2x and thisnegative 9x right over there. So we will get negative 7xplus 3 is equal to negative 7x. So 2x plus 9x isnegative 7x plus 2. Well, let's add-- why don't wedo that in that green color. Let's do that inthat green color. Plus 2, this is 2. Now let's add 7x to both sides. Well if you add 7x tothe left hand side, you're just going tobe left with a 3 there. And if you add 7x tothe right hand side, this is going to goaway and you're just going to be left with a 2 there. So all I did is I added 7x. I added 7x to bothsides of that equation. And now we've gotsomething nonsensical. I don't care what x you pick,how magical that x might be. There's no way that that x isgoing to make 3 equal to 2. So in this scenario right overhere, we have no solutions. There's no x in the universethat can satisfy this equation. Now let's try thisthird scenario. So once again, maybe we'llsubtract 3 from both sides, just to get rid ofthis constant term. So we're going to get negative7x on the left hand side. On the right hand side, we'regoing to have 2x minus 1. And now we can subtract2x from both sides. To subtract 2x fromboth sides, you're going to get-- sosubtracting 2x, you're going to get negative9x is equal to negative 1. Now you can divide bothsides by negative 9. And you are left withx is equal to 1/9. So we're in thisscenario right over here. We very explicitlywere able to find an x, x equals 1/9, thatsatisfies this equation. So this right over herehas exactly one solution.
