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Systems of Equations Test Prep Video

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Systems of Equations Test Prep Video

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try guys Christy  test prep video with the solutions should get you ready for the test tomorrow  here we go first problem we are given the following system of two linear equations fifth six- worth solution to the system let's chat so we know that this is act  submissive why  so going to do if we just going to plug these both in going to plug accident where X goes 249 x axis 6  crossword X Y wives negative for ruin see if that equals -2  5 10 * 6 is 5413 * -4 is -52 equals to 54 - 52 to sew the first one work shut the second one  -3 - 5y sequel still so it's plugging RX equals 6 year send r- for here check this one if 3 * 6 is -18 negative five times negative Force positive 20 -18 + 20 is in fact two so two equals two Psalm so that one works right next one next problem solve systems of equations graphically it's the way I've shown you guys how to do these It Is by putting in slope intercept form for each one of in slope intercept form I'm going to rewrite them down here and then let's just all them listening to a taxable side imma get -3 y equals positive X  + 9  just a reminder that those don't combine the X and the nine combine the not like burnt now I'm going to divide every term by -3 that's going to give us our y by itself  X over negative 3 so remember there's a one in front of the sacks for this is this fraction here is like a 1 over negative 3 or just negative 1/3 so going to write a beautiful one third Act  9 divided by -3 is -3 so those are first-line and now let's check our second one before this one we're going to subtract 6X from both sides so they don't cancel I would end up with negative 6y equals -6x -6 divide everything by -6 circuit Y equals X crossword  so now we just need to graph these few lines right here and see where they intersect that's how you solve equations okay  what's the definition graphically is the point of intersection is the point that is the solution to equations for here we go we have negative one third x -3 so 1/2 we start at negative 3  Shimmer start here start this year my office has a y-intercept right here negative 3 so going to go 1 - -3 and my flow is up one write 3 stopped up one left three two negative slope right stop one left three so there's that one could put a line on that triple does that equation Ellis cross the other one silicon startup recall X plus one flavor point there and are slope is just one over one make some points here so start here Sonic X + 1 so much slope is 1/1 let me write that in sloping 1 / 1 so you go up one right one 4 down one left one track down one last one  someone left one so you free are intersection points going to be right there  just go ahead now process so my my they're such a points right here it's negative -3  -2 search trippy check -3 negative 2 and the app it should work out so if I do my mental math here that -3 negative two would work in both these equations just like I did number one so next problem solve the following system of equations were using elimination basic that tells me that we're going to eliminate one columns as you can see right here  positive t y -2 y when I add those together we're going to cancel out so that's the whole idea here is that we're just going to add straight down each column like I said 2y - 2y that cancels out that's the whole goal is that one of these columns cancel themselves out and -3x 5x of -8x inches equals 80 divide both sides by -8 taxis going to equal -10 so now what you need to plug back in and solve for y guy so negative 3 let's let's use the first equation we write it out here  transfer Club this -10 in here for x sulfur why so this is 30 + 2 y equals 56  Dark Thirty from boss 2 y equals 26 live beside the bike trail and why is going to equal 13 the negative term 13 Houston's my answer Star Party checked it before this is true Schnucks Page solve systems of equations elimination advance for going to do I'm going to coming to eliminate for both very just to give you some extra practice and to show you so it's what we're going to do the copy and paste that send so we're going to in one of these were going to eliminate X  and then one of them were going to eliminate why commercial eliminate X in this will eliminate y k here we go so we're going to live in a Texan this one  4 multiply this one by 7 and this one by 6 so it's rewrite these 7 x 6 x is 42 X 7 * -5 -35 y 7 * -32 just going to be negative 224 6 * -7x is -42x 6 * 8y 48 y 6 * 46 276 China we're going to cancel out the axe and just add straight down we are going to get 13 y equals 52  divide both 13  7 y equals 4 this one on this we're going to just pick this time Morgana X positive 8 Positive Vibes Church rewrite this one this would be 48  cracked -40 w equals 256  Grant richest multiply in these out 5 * -7x is -35x 5 * 8 y 40 y 5 * 46 230 I believe so this gives me 13x equals -26 divide both sides by 13  Xanax is going to be  -2 come to check them real quick on doing this whole Mass  secretive 4 - 20 14 + 32 stroke a good they work so ask equals -2 cycles for next problem in this one some of your having some hard times on these cuz Okay says that  choma and Ryan's teacher gave them a system of linear equations to solve each a few steps that led to the system shown in the table below so the teacher has this these de system 3x + 8 y equals 0 7/2 - 11 y equals 4 the first off let's see if she Oma's matches the teachers okay the first thing no this is that she almost first equation in the teachers first equation or identical okay so those are definitely equivale they're identical their equivalent so let's just put a little green Mark next to the first one  search Shannon now it's look at the second one remember I can multiply any equation by any number and get an equivalent equation or I can add if I can how to be two equations together what would I get so I can see that if I add these together 3 x - 7 x makes -4x K 8 y - 11 y. Makes -3 y and 0 Plus for that makes for so you see if I add both of these together I get cheeonas second equation right here okay so this is also equivalent  so you're going to notice that Ryan's first equation is the same exact equation that I'm chiona has over second equation in the same exact equation that we have when we add the teachers two equations together the one right here in the blue right those are identical so this is also equivalent but then whenever we look at the second one on Ryan's this is -7 -11 y equals 0 + teacher second equations of -7x - 11 y equals 4  there's no play search the teacher second equation  send Ryan second equation could ever be the same there's no way can't happen because the left sides exactly the same the right side two different so no matter what happens though what they would never be the same so that this one is in so now as a result the only one that has equivalent equations Shoma  how to say that name  Schnucks Schnucks Page here we go I'm going to systems using substitution I'm going to be one of these or maybe the second one the second one is solve for x so what I'm going to is because -3 y + 8 is the same as axe I'm just going to plug it in right where the exit right there somebody get -7 fun do we go -3 y + 8 I'm just substituting it where the x is in the first equation in words for the if you look here you can see that everything's in terms of why now so bum 7 * -3 why is 21 why -7 times positive 8 is negative 56 slander solving for y right now  21 y - 6 y That's a 15 y 56  sequels for this combining like terms and this step  you can add  50 next about sides so 15y equals 60 survived both sides by 16 send y equals 4 current social support listen to the second equation x equals negative 3 x 4 Plus Fox equals -12 CrossFit equals negative for some answers x equals -4 y equals 4 you can check using the equation do some Mental Math here real quick and you're going to see them at work I encourage you to check out the mental math yourself as well okay I did in my head Google Maps satellite Solutions of the systems of equations graphically switchgrass go to this y equals 9 X -5 if you remember that whenever you graph equations play have the same slope and different y intercepts they're going to from Venus Solutions but I'm going to show you that graphically Sarah graffam so let's make sure we do that search first what's graph 9 X -5 so one two three four five we're going to go up 9 I'm right one 1040 cross that line Turf not reform x19 x + 6 so 24626 I'm going to go down 9 come right one show me the graph this one now just pick a different color to purple guess you can see these are parallel lines and I'm going to be no sun home next one  graph the following system of linear equations and determine its number of solution so we're going to do this one was put the first one in slope intercept form Providence attraction action both sides vinegar to y equals -10x -8 divide everything by 2 you're going to get y equals -5 x -4 as you can so we have y equals -5 x -4 as you can see we get the same stock equation twice so just going to get one line on top of another line  so 1 2 3 4 go up to go up one two three 5 + 1 Santa's going to be the line we're going to have  foam home  I'm basically all we're going to do is grab that line twice so what happened there where duplicated that let's just doing weird stuff here the scrap another one room will grass brown one about. Chicopee idea we have one line on top of another line as a result we have infinitely many solutions say one line on top of another line that's what happens the infinitely many Turf coming up to Rusty the next ones cuz the bells about to ring this one have different slopes besides different slopes how to resolve will have one solution okay I'm not going to grab it I don't have time but I heard you Ralph it over here and see that intersect in exactly one spot this one here let's let's graph web sources analyzing the systems of equations algebraically how many solutions does the following system of linear equation you can see right here I have A+ 9y here so what's going to happen is whenever I go to put this in slope intercept form you have different 12th because these call officiants are different which makes sense if these coefficients are the same in front of the Y and the ones in front of the acts are different  Diesel have different slopes he's not different slopes looking to have exactly one solution search  the next one you can see here once again in front of the Y variable patients are exactly the same  Shannon front of the acts are also exactly the same so what does this tell me a tells me that these are going to have the same slope sir  so but whenever I saw these for why what you notice is these numbers over here are different so these are wines so not the same line they have the same flow same slow but the equations are different search for think about that because the slopes will be the same but the equations are different there going to be no Solutions so this next one if you notice on this one if I If I multiply the second equation by -2 I will get -6x before y equals 2 and if you notice these are the same exact equation as a result of five infinitely many solutions  you have to recognize this whenever you see it on the test or you can can smoking a subform if you have to recognize that if you multiply one of them by a number and you get the other equation that's that's the definition of infinite how many solutions does the same line I just written a little bit different then our final problem here as solve any teach systems of linear equations how many Solis does the following system of linear equations have the bells about to ring so what I'm going to do is I'm going to home cure  and then what we're going to do is it going to write the second equation in standard form and I'm in a machine -4x equals 16 - 14 y transporting multiple sides -4x + 14 equals 16 call Tractor shop there is the Bell if I want to play stop equation by 2 what you'll notice is I'm going to get the second equation here sharp focus is going to be infinitely many solutions as well okay alright hope you enjoy the video

Uploaded by Paul Blazi. Listed in Mathematics

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