Videos

Ch5 practice test

Added Jan 30, 2020 •

Copy this URL:
Embed code:	<iframe class="edlio-embed-player" type="text/html" width="640" height="360" src="//ehs.leusd.k12.ca.us/apps/embed/?v=235160" frameborder="0" allowfullscreen></iframe> Change dimensions

Show Transcript

hey this is the practice test for chapter 5 on question number 1 use the graph to solve the system of linear equations check your Solutions so we are looking for where do the two graphs cross what point do they share and they cross right there down at 0 negative 2 remember if you have an occasion where two lines are parallel to each other will be a no solution on that cross or two lines end up being the same equation so you really have one line on top of the other then it's a infinitely many solutions unquestioning is the ordered pair a solution of the system of linear equations so we want to know if 2/3 is the point where if we were to graph these two were if they would cross their sew in set of having a graph when we can plug it in if it makes a true statement for both then that means that point is the solution so we're going to plug into 4X and 3/4 wide so -2 * 2 + 3 * 3 is equal to 5 -4 + 9 is equal to 505 is equal to 5 works for the first one that's check the second one 3 * 2 + 2 * 3 is equal to 12 6 + 6 is equal to 12 and that works out as well so it works for both so yes it's a solution hey let's look at question number 3 I'm is for kind of 1 a solution to this system so we're going to do the same process we're going to plug it in for X and Y see if it works for both in the first one negative 4th + 1 is equal to -3 and so we get -3 equals -3 at works let's try the second one we get 4 + 3 * 1 is equal to 6 so we get 4 + 3 is equal to so we get seven which does not equal  so because it didn't work for the second one this is no not a solution okay let's look at question number four graph and check to solve the linear system by graphing these we need these both to be solved for so let's take a look at that first equation negative 2x + y is equal to 1 add to x to the other side so that first equation becomes Y is equal to 2x + 1 now that second equation for that second equation we've got to -2 experts to the other side so 3 SO3 is equal to -2x + 11 / 3 we get Y is equal to -2/3 x + 11 it's super great one to graph for that second one you know as a decimal 11/3 is at 3 and 2/3 this would definitely not be one that I would suggest to graph I'm if you have two we're going to do the best we can on this let's grab that 2x + 1 I'm going to start there we're going to go up to over 1 up 2 over 1 and here's our first graph let's look at it our second one I'm so 11/3 is about 3 + 2/3 it's going to be up here and then from there we're going to go down to to the right 3 and I'm looking at that it it looks like cross at that point and we could solve this another way to double-check but they will indeed cross at that one, one two three one, three and intestate you get something weird like that definitely take the time plug that point back in to both of them just like we did in the previous two okay question number 5 which inequality is represented by the graph we've been doing a lot of these in class lately so we've got a dotted line so let's look at our places we've got to know what we see and hear all our choices are 2/3 x + 1 cases there's no change in the equation on those choices that is in fact 2/3 x + 1 about the shading and think about whether this is a solid or dotted line since this is dotted line we that means we do not use the equal bar so we can cross off a and b now we want to know is it greater than like in C or less than as in Choice T go to that y-intercept since everything is shaded above that line it's going to be great for our final answer is Y is greater than 2/3 x + 1 I saw the system of linear inequalities check Your solution so you can choose most likely you want either substitution or elimination you could if you really wanted to graph as well if you have graph paper at home feel free to try the and check your work that way too since they're both set up y equals I think of substitution so let's plug in since they're both y equals we're going to play x - 2 in for that bottom light so x - 2 is equal to 7x + 10 so our whole purpose for using one of these method is so we can solve an equation with just one variable hey so let's get X's by itself so minus X to both sides so we get -2 is equal to 6X + 10 10. and we get -12 is equal to 6 x so that means X is equal to -2 / 6 so once we get there taxes -2 let's go back you can use either one of these two equations plugin -2 / X solve for y so why is equal to -2 - 2 so why is equal to -4 so are finally answer is negative to negative 4 a question number seven since this is another one where you have y equals substitution is probably more preferable so let's take the -5x - 1 since it's equal to Y and let's put it into that top why I'm going to rewrite that topic reason is 3x + 4 parentheses -5x - 1 and so 3x - 20x distribute that 4 - 4 and I forgot to write that equals -38 equals -38 combine like terms if they're on the same side -17x - 4 is equal to -38 at 4 so is -17 X is equal to the difference is -34 or negatives and positives divided by -17 and so we get X is positive 2 it's so you have access to let's plug it back in for y so why is equal to instead of -5 -5 * 2 - 1 so I'm taking the x value plugging it into that bottom equation to find y Sol Y is equal to -10 - 1 Y is -11 so our final answer for that one is two, negative 11 question number 8 of I say you know either way you could use substitution to solve for that tap X and then plug it into the bottom or what do elimination you could get your access to cancel by multiplying the top equation by -4 that would cancel out the positive for and with the wise while if the top why was a negative 10 which is we need to multiply by a negative 2 to everything then we could get the wise to cancel so we've got a lot of options on this one since we got three other way that look like you know we probably could use elimination on there and let's practice substitution one more time so I'm going to take and solve for x and I'm going 2-5 y to the other side so X is equal 2 - 5y and now I'm going to plug it into the bottom equation so instead of four times now I'm going to plug in 7 - 5y so 4 * 7 - 5y + 10 Y is equal to 18/7 * 4 is 28 - 20 don't forget to distribute the four to the second term + 10 Y is equal to 18 combining like terms so you got -20 y + A+ 10y which is -10 Y is equal to 18 -28 to both sides we get -10 Y is equal to negative divided by -10 wise one okay now let's go back and plug it into this x equals equation so x equals 7 - 5 * 1 so x equals 7 - 5 x equals negative 2 so we get negative 2, 1 for your final answer can rats jump up time to question number 9 next since we're solving this is a eliminate against all for substitution we could solve the top 1 4X let's practice this one with elimination so we look at how we could get the axes to cancel where to add to zero I should say so if this bottom term is 2x we need that tapped him to be a negative 2x so we're going to reply that whole topic lesion by -2 so all the terms get multiply to -2 that means that becomes negative 2x -2 * 3y is -6 y negative 8 * -2 is -4 rewrite that bottom equation right underneath 2x + 4y is equal to 0 now we can add up our columns axes go away -6 y + 4y is -2 y -4 + 0 is -4 divided by -2 the Y is equal to positive to negative divided by 9 the positive then go ahead you can pick either equation the multiplied form the original form and solve for x I'm going to use that original topic lesion so you have X + 3 x y and now we know why is 2/3 * 2 is equal to -2 so x + 6 is equal to -2 -6 both sides so X is equal to -8 and our final answer then is -8 positive 2 a question number 10 now this one is kind of nice we'll look at I already see the X's cancelled and everything's lined up so let's see what happens we add up or exes that cancels you get a zero the only thing is we had it for a why is that gives you a zero so on the left side taxes and Y cancel zeros equal to 5 + 5 is 10 so this is one of those weird ones 0 does not equal 10 so this is a no solution what's really going on if we look at the graphs of both of those is that they're going to be parallel they're never get across so if you get a false statement something like that it's a no solution okay number 11 tuyet using eliminations nothing's going to cancel out let's take a look at this you want your ex has to cancel out if you get a deposit 8 in a positive for well that would if the bottom X were a negative 8 then it would cancel so 4 times what will give you a negative 8 so we're going to multiply that bottom equation by -2 that we could figure out with the wise what to cancel as well the rewrite that topic lesion do we have a tax minus Y is equal to 16 and we get -8x and negative 2 times negative wires + 2y AMC * 8 is -16 this is what either one of those weird ones your ex's ad20 your wise ad20 so you get 0 equals what's 16 - 16 + 0 now this is a true statement 0 does equal 0 so if you get something like that these are really the same equation if we solve both of these for why they're exactly the same this is just a multiple of two of the bottom one so what you get is a line on top of another line so you start with one line and then the other line is exactly the same so this would be infinitely many solutions okay question number 12 graph the inequality now there's no grass on here so we're going to add this in so you going to make your coordinate plane trying to make it as neat as you can or just add in some graph paper that is usually the best and go to start now but we can start graphing points don't fill in your line till you decided whether this is a dashed line or a solid line and because there's an equal bar right here that mean it's going to be a solid line and then later on when we do our shading we have to know whether to shade above or below that line so since it's Y is greater than or equal to greater than is going to be above so solid and above let's start marking your points on here equals MX plus b squared and y intercept of negative to soap as a positive slope should be going up as you go left to right up to over one up two over one up two over one I work at backwards as well so make some points on their this is a solid line and since we're graphing above go to that Y intercept and then we want to shade above that line so that case it's going to be this section that she did Kanto number 30 graph the system of linear inequalities so going to get her coordinate plane setup so I'm the first part Y is greater than or equal to one because it has that equal bar this one is going to be Dash or I'm sorry salad and then greater than it's going to be a bug and on the bottom one no equal bar there so that one's going to be dashed and less than means it's going to be below now grabbing the first one y is greater than or equal to one so noticed that's one where you don't have accent it so that means asking me anything but why is always going to be equal to 1 this is a horizontal line go to that y-intercept of one and it's going to be that solid line now greater than or equal to means we're going to be shaving everything above that line I'm going to hold and that cheating until we put it all together so I'm going to grab the next grass in blue -2x + 4 maybe a dashed so as we have points you want to make sure you don't fill it in yet so one we were going to start at positive for 1 2 3 4 and then this is a negative slope so down two over one down two over one or up two to the left one and once you get some points on there when a dry dash line Sorry my grass are a little the ones you'll have an attached you already have your coordinate planes in there for you and now on the blue line why is less than so less than go to that Y intercept and everything would be shaded below so I mean we would start with the first graph me to start changing that and yellow the first graph is going to be above so so this should be a bug for the blue graph would be shaded below I'm going to do that in green so you go to the Y intercept and below so what is shaded for both run out of colors here what shaded for both I'm going to use black on that is going to be this intersection right here so check the graph that you tried should be that intersection do you want to make sure to highlight on the test highlight that area which got double shaded I'll add two questions I'm so these ones we set up two equations so and the first one you spend 264 bucks on clothes shirts cost $24 and Pants cost $32 and you buy a total of 9 items so like most of these Pro that we've done for the amount of something somebody use asked for the number of shirts always label your variables and P4 the number of pants hey so it's a total of 9 items so the number of shirts asked plus the number of pants p is equal to 9 there's our first equation figure in the cost will eat shirt cost 24 bucks so it's going to be 24 x how many shirts we have each pair of pants cost 32 x 2 + 32 p equals 264 so there's our system there's our part 8 now it says they solve by graphing interpret Your solution I'm going to tell you just to ignore for the graphing part this one's not super nice to be solving by graphs so just ask that out we're going to solve this week it would probably be easier to either solve it by substitution or elimination let's do this one was substitution which means that we need one equation either solve for us or solve for Pete so I'm going to take that top equation I'm going to solve that for Pete and rewrite that as p is equal to in a minus as to the other side 9 - x and then let's take that 9 - Essence is equal to p and plug it into that bottom equation and multiply it to the 32 so now we're going to rewrite the bottom equation 24 right that over here 24 s + 32 * 9 - s 3.9 and 4 Pete is equal to 264 we're going to distribute that 32 the 24s 32 * 9 is 288 -32 s is equal to 264 combine your s term so 24s -32 us so come by not to get Negative 8s + 288 is equal to 264 -288 to the other side so we get Negative 8s and that's going to be a difference of 24 but we're subtracting a bigger numbers -24 and some corn to know for these questions if we ended up getting the number of something was equal to a negative we may want to go back and check our work because here we're going to get negative divided by negative is a positive and we're going to get S is equal to 3 which means we bought 3 shirts but if we get a negative go back and make sure we did everything correctly check your work maybe redo it South after 3 we bought a total of 9 items while 9-3 will give us how many pants that's going to give us 6 pants so our final answer would be nice shirts and 6 non starry night night shirts three shirts and six pairs of pants okay 15 you're selling tickets for a high school concert student tickets cost $4 and a general admission ticket cost $6 right there right when you figure out what are the two things were talking about two different types of tickets I'm going to say s Christine tickets and general admission so I'll say g equals general admission tickets okay sweet. Or two variables next okay so we remember just like here we have the amount and we have the cost so let's for the amount so you sell 450 ticket so that the amount of tickets so that means S Plus G is equal to 450 now let's look at the cost what's this tune tickets cost for Buck's soap or s+ general tickets cost 600 + 6 G and how much money do we bring in 2340 now since we saw the last one by substitution let's practice this one with elimination but you could saw their like the last one either solve the top equation for us or you could saw that 4G I'm going to try this with elimination for instance so if we wanted to ask his to cancel out or to add to zero the bottom is for we need the top one to be a negative we're at so we can multiply that top equation by -4 so let's rewrite that top equation so -4 s -4 G and then for 50 times a negative so that's going to be a negative will double 450 you get 900 and we need two groups of those so negative 1800 and then recopy the m-14s + 60 is equal to 2340 now our  are good to add to zero at a bar cheese we positive to G is equal to we need the difference between 2340 and -18. And when we subtract those more we get end up getting 540 I will be a positive more positives and negatives write 2 G is equal to 540 / 2 so we get 270 so we have 270 General Open tickets remember they have to add up to 450 S Plus g equals 450 so we have S + 270 is equal to 4/5 -270 so  is equal to we subtract those we get a hundred and eighty so unless we would have Trinity student tickets 270 general admission

Uploaded by Nikola Leibold.

Home
Photo Album
Videos
Posts

Videos

Ch5 practice test

More videos from Nikola Leibold