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Current time:0:00Total duration:7:16

Video transcript

we're asked which of these strategies would eliminate a variable in the system of equations choose all answers that apply so this first one says add the equation so pause this video would adding the equations eliminate a variable in the system alright now let's do it together so if we add these equations we have on the left hand side we have 5x plus 5x which is going to be 10x and then you have negative 3y plus 4y which is just a positive 1y or just plus y is equal to negative 3 plus 6 which is just going to be equal to positive 3 we haven't eliminated any variables so choice a I could rule out that did not eliminate a variable let me cross it out and not check it subtract the bottom equation from the top well when we subtract the bottom from the top 5x minus 5x that's going to be 0 X's so I won't even write it down and we've already seen we've eliminated an X so I'm already feeling good about choice B but then we can see negative 3y minus 4y is negative 7y negative 3 minus 6 is going to be negative 9 and so choice B does successfully eliminate the X's so I will select that choice C multiply the top equation by 2 then add the equations pause the video does that eliminate a variable well we're gonna multiply the top equation by 2 so it's going to become 10x minus 6y is equal to negative 6 and you could already see if you then add the equations 10x plus 5x you're gonna have 15 X that's not gonna get eliminated negative 6y plus 4y is negative 2y that's not going to be eliminated so we can rule that out as well let's do another example 1 they're asking us the same question which of these strategies would eliminate a variable in the system of equations the first choice says multiply the bottom equation by 2 then add the equations pause this video does that work alright so if we multiply the bottom equation by 2 we are going to get if we must by - we're gonna get 2x - 2 - 4 why I should say 2x I'm just multiplying everything by 2 - 4 y is equal to 10 and then if we were to add the equations 4x plus 2x is 6x so that doesn't get eliminated positive 4y + negative 4y is equal to 0 wise so the Y's actually do get eliminated when you add 4y - negative 4y so I like choice a and I'm gonna delete this so I have space to work on the other choices so I like this one what about choice B pause the video does that work multiply the bottom equation by 4 then subtract the bottom equation from the top equation alright let's multiply the bottom equation by 4 what do we get we're going to get 4x minus 8y is equal to 20 yet we multiplied it by 4 and then subtract the bottom equation from the top so we would subtract 4x from 4 X well that's looking good that would eliminate the x's so i'm feeling good about choice B and then we could see if we subtract negative 8y from 4y while subtracting a negative the same thing as adding a positive so that would actually give us 212 Y if we're subtracting negative 8y from 4y and then if we subtract 20 from negative 2 we get 2 negative 22 but we see that 4x minus 4x is going to eliminate our x's so that does definitely eliminate a variable so I like choice B now what about choice C multiply the top equation by 1/2 then add the equations let's try that out pause the video all right let's just multiply times 1/2 so the left-hand side times 1/2 we distribute the 1/2 is one way to think about it 4x times 1/2 is going to be 2x plus 4y times 1/2 is 2 y is equal to negative 2 times 1/2 is equal to negative 1 now and then they say add the equations so 2x plus X is going to be 3x so that's not going to eliminate the x's 2y plus negative 2y well that's going to be No so that actually will eliminate the Y's so I like this choice as well so actually all three of these strategies would eliminate a variable in the system of equations this is useful to see because you can see there's multiple ways to approach a solving a system like this through elimination let's do another example which of these strategies would eliminate a variable in the system of equations same question again so the first one they suggest is subtract the bottom equation from the top equation pause this video does that work well if we subtract the bottom from the top so if you subtract a negative 2x that's the same thing as adding 2x just you're adding 2x - 3 X that's 5 X the X's don't get eliminated subtracting 4y from negative 3y is just gonna get us to negative 7y the y's don't get eliminated so I would rule this one out nothing's getting eliminated there multiply the top equation by 3 multiply the bottom equation by 2 then add the equations pause the video does that work alright so if I multiply the top equation by 3 I'm going to get 9x minus 9y is equal to 21 and then I find multiply the bottom by 2 so this is times 2 I'm going to get 2 times negative 2 is negative 4x plus 8y is equal to 14 and then they say add the equations well if I add 9x - negative 4x that doesn't eliminate the X's that gets me to a positive 5x and if I add negative 9 wide a positive 8y that also doesn't eliminate the Y's I guess me - a negative Y so choice B I can also rule out once again deleting all of this I have space to try to figure out choice C multiply the top equation by 2 multiply the bottom equation by 3 then add the equation so they're telling us to do it the other way around pause the video does this does this work alright so we multiply the top equation by 2 and we're going to multiply the bottom equation by 3 so the top equation times 2 is going to be 6x minus 6y is equal to is equal to 14 and then with this McQuade when you multiply it by three both sides that's the only way to ensure that the equation is seeing the same thing is if you do the same thing to both sides that's really the heart of algebra so negative 2 times 3 is negative 6x and I already like where this is going because when I add these two they're going to get eliminated plus 4y times 3 is going to be plus 12 y is going to be equal to 21 and then they say add the equations well you immediately see when you add the X terms on the left-hand side they are going to cancel out so I like choice C