Whenever i need to use an equation. I should always make sure that i solve it for y right, because if we ever need to put it into a calculator or judge what our slope or y intercept or anything like that is, it has to be solved for our y for us to know that Information so my first one is 2x: minus 3y equals 0.. So i subtract 2x on both sides and i end up with negative 3y equals negative 2x, and then i divide both sides by negative 3 and i get y equals two thirds x. A negative, divided by a negative makes it positive and then for the second one. I subtract x on both sides and i end up with 2y equals negative x minus seven. I divide everything by two and i get y equals one half x minus seven over two now to figure out which graph is representing these two equations. I need to put them into my calculator so if you’re online you’re going to be using desmos, so we’ll go to desmos.com and we’ll open up our graphing calculator and we’ll put in our two equations, so y equals two thirds x and y equals one half x. Minus seven over two i’m, sorry that should be negative one half x, that’s, where i’m going. That should be negative one half x. So if we look at that graph – and we compare it with our answer to this – it seems like answer.

Choice d would be our same graph, so this should have been a negative here and it would be answer choice. D number: two: if the system of linear equations two x plus y, equals one and y equals negative, one, half plus one are graphed on the same coordinate which of the following is the solution. So the solution right is where our two graphs intersect each other that coordinate where they cross, where they meet, where they touch so i need to solve 2x plus y equals 1 for y. So i subtract 2x on both sides and i end up with y equals negative 2x plus 1.. So now i can put these two graphs in my calculator y equals negative one half x, plus one and y equals negative two x plus one, and i need to see where those two graphs intersect each other, so i’ll go to desmos and i’ll put in those Two equations y equals negative one: half x, plus one and y equals negative two x plus one, and we want where those two graphs are intersecting each other. So this coordinate right here is zero, comma one, and that is not one of our solutions, so it would be d not here. Okay, the length of a rectangle is equal to triple the width. Okay, so we’re saying the length so we’re speaking specifically about the length is equal, so we have our equal sign triple means times three and then the width so triple the width which systems of equations can be used to find the dimensions of the rectangle.

If the perimeter equals or the perimeter is 85 centimeters, so perimeter equals 2l plus 2w and perimeter is 85, so 85 equals 2l plus 2w. So these would be the two equations that i’m looking for. So i can already narrow it down to h and g because we have l equals 3w. The second two equations look a little bit different, so we can factor out a 2 in our equation for a perimeter, so we could say 85 equals and then, since they both have a 2 in there, we can take the 2 out and use it as distribution And then length, plus width, which would look like letter h g would not be correct because it’s 2 times our length plus two times our width not six times our width, an online digital game and movie company rents, video games for 4.99 and movies for 2.99. In one hour, the company rented a total of 35 games and movies if the total rental income for this hour was 144.65 cents, not including tax, which of the following statements, is a reasonable conclusion. So before i even read those conclusions, i want to start off and kind of write down the information that it gives me. Okay, so video games are 4.99 and movies are 2.99 and i know movies, plus video games equals 144 or sorry it’s, not just simply movies, plus video games, it’s the cost of the movies and the cost of video games so 4.

99 times. The number of videos plus 2.99 times the number of movies equals 144.65, so the total rental income for movies in this hour was 99.80, not including tax. So, in order to figure that out, i have to solve my systems of equations, and i don’t want to do that. Yet there were more movies than video games rented in this hour there were more video games and movies rented in this hour. The total rental income for video games in this hour was 74.85, not including tax, all right so i’m going to have to actually solve the system of equations. So i know my movies plus video games equals 35.. So i want to solve this for one of my variables so i’m going to go ahead and i’m going to solve it for m okay, so i subtract b on both sides and i end up with m – equals negative v plus 35. Now, if i look at my other one, i need to solve it for m as well, and then i can put in my calculator. I can treat this as like y equals. So first thing i do is i subtract my v and we end up with 2.99 times our movies equals negative 4.99 times our video games plus 144 144.65, and i divide everything by 299 and so that’ll give me m equals our video games divided by 299, plus Our total cost divided by 299. So now i can put these two in my calculator, so my m value is my y and my v is my x.

So then y equals it’s negative of x if i negative x, plus 35 and then in my second equation. It’S negative 499 v divided by 299, so y equals negative 4.99 x, divided by 299 whoops and then plus 144.65, divided by 4.65, divided by 299.. Okay. So i need to look at my graph. I need to find where my intersection is because that coordinate is going to give me what my values are so it’s, 20, 15., so 20 and 15.. So my x value in this case right was my video games and my y value is my movies. So there were 20 video games and 15 movies that were rented. So now we have to go back through these. The total rental income for movies was 99.80. There were more movies than video games that were rented that one’s definitely not true. There were more video games that were rented than video. There are more video games and movies that were rented in this hour that one’s definitely true. In 2004, a married couple could have calculated their estimated income tax for that year. Using the equation, t equals 0.25 c minus 6525, in which c represents their combined taxable income. The married couple had a combined taxable income between sixty thousand and sixty four thousand, which of the following is the reasonable amount for their income tax, so we’re going to put each of these into our equation so that we can see which of these answers falls within Our range okay, so t equals 0.

25 and then 60 000 minus 6525. So if i were to put that into my calculator so 0.25 times, 60 000 minus 6525 – that would give us 8475 and then i do the same thing with the higher rate. So 2 equals 0.25 times: 64. 000 minus twenty 6525. So zero point two five times: sixty four thousand minus six thousand five hundred twenty five, and that gives us nine thousand 9475.

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