6 4 Elimination Using Multiplication Pre Algebra Ember Learning Labs

last lesson of this unit we're going to do elimination with multiplication so we're just going to finish up our discussion of elimination and look at what if it's not already set up all nice and pretty for us so let's take look with couple examples example one we're going to solve both systems using elimination we're going to start with the system 5x plus 6y equals negative 8 and 2x plus 3y equals negative five okay so said in the last lesson that the first step is to make two of the variables opposite well the first step really is to get it set up like this where we've got variables stacked on top of each other and and just numbers by themselves so essentially we put them both in standard form right is is what we're going for there now so in order to get them to be opposites we need to take and we need to multiply one or both of them times number so if take and look at this second one and multiply it times negative two then these two are going to be opposites right because negative two times three is negative six so we're going to multiply times negative two negative two times two is negative four negative two times three is negative six negative five times negative two is negative excuse me positive ten almost made mistake even make negative mistakes right and so that's this one changed so let's rewrite this first one underneath plus 6y equals negative 8. so see now we're set up all pretty for elimination so we're going to do the elimination step these two cancel negative 4x plus 5x is positive 1x or just nice 10 minus 8 is 2. so we've already got it wow that was that was nice problem wasn't it so we're going to take and substitute that 2 in for in any of the equations would not if were you put it into one of the ones that you multiplied because those numbers are going to be bigger because you you multiply them times something and made them bigger and so i'm going to plug it back into one of the original two i'm going to plug it into the second one you could do it into any of these actually so i'm going to plug it into the second equation right and have 2 times parentheses plus 3y equals negative 5. i'm going to put 2 inside the parentheses and then solve it on down 2 times 2 is 4 plus 3y we're going to bring down what we haven't touched negative 5. we're going to subtract off this 4. because it's positive so to get rid of it we're going to subtract it it's positive and it's that addition subtraction right because the 3 is also positive but we're going to divide it off in minute negative five minus four the signs are the same so we add and keep the sign so be negative nine we're gonna divide by three on both sides leaving us with equals negative three we just need to write the equation excuse me the answer as point and then we're done with this problem so it's the point two negative three because points go circle that dude let's do one more and then we're going to be done with this lesson and this unit sound good think so sounds great let's do example number two we're making great progress here folks hope y'all are enjoying it like comment subscribe would would be great if you're especially if you're just joining us on youtube and you're not one of my students because love to hear from you love to hear from you whether this is these videos are being useful to you or how you're using them or if there's anything else we can help you with on your math journey your science journey or your homeschooling journey in general or if you're teacher using this in your your class or something i'd love to hear that too so our example 2 is 4x plus 2y equals 8 and 3x plus 3y equals 9. now this one's not quite so simple right because this one we can't just multiply time one of them and then have it have it end up being the other one so on this one we need to multiply both of them times something right so we can if we wanted to eliminate the x's we could multiply the top one times times three and the bottom one times negative four that would do it right and make both of them make these 12 and negative 12 respectively or we could do 3 on the top one and negative 2 on the bottom one and we'd cancel the y's which think is the choice that i'm going to go with just really just because those numbers are smaller it really you really could pick either one so the top one i'm multiplying times three and then the bottom one i'm going to multiply times negative right so picked these numbers but made this one opposite right so we're going to end up with 6 and negative 6. so let's do that don't forget to multiply times everything that would be another another common mistake that see on this kind of problem especially if you get to going too fast or any of that stuff if you if you you is is not really distributing this all the way so we've got to do 3 times everything on the top 3 times 4x is 12x 3 times 2y is 6y 3 times 8 is 24. that's one of those multiplication facts that always have to double take and think about for half second you'll have have ones like that if you do what are your double take multiplication facts let me know in the comments negative 6x don't know why i'm so chatty in this particular video just this happening maybe it's because i'm hungry and i'm trying to distract myself because am definitely hungry negative 2 times 3y is negative 6 equals 9 times negative 2 is negative 18. that would be extra special easy way to easy place to forget is not multiplying this last one i've seen that mistake made many many times so now we're to the elimination step because these are going to cancel right so over here we have 12x minus 6x so that gives us 6x this one's not quite so nifty as the first one because we we do have that last little step in minute 24 minus 18 is six okay so the last thing we're gonna do here is we're going to divide both sides by six those sixes cancel leaving us with equals now six divided by six is one right so it kind of cancels two sort of but when we're dividing canceling equals one right so we're going to take and we're going to substitute this one in somewhere i'm going to plug it in in the second one mostly because it's easy to draw the arrow honestly on on this particular one it's easier for me to get at it and it's gonna be less messy on the on the picture and for the notes and such right so i'm gonna do the second one with parenthesis where the is equals 9. we're gonna stick one in there that's nice and easy we like ones and zeros ones and zeros make our life easy three times one is three plus three equals nine we'll subtract off this three those cancel leaving us with three equals six can divide that three off leaving us with equals two last thing that we're going to do in this lesson this unit is to write our answer as an ordered pair one two because ordered pairs go they don't go bumping the night they go xy if you're not one of my students thanks for joining us you can check out emberlearninglabs.com for more information about the things that 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