1. 10:25

from Jonathan Klos Added 0 0 0

In this video, we look at a word problem that can be modeled by a linear system of equations. In this problem, there are two different trips to the store to purchase hotdogs and buns, and we are given information about the total costs of both trips and asked to determine the price of a pack of hotdogs and buns. We first define our variables, and then translate the problem into the right linear system that we can solve. We use the elimination method to solve our system, but then need to go back at the end and answer the question we were given in the problem.

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• 07:30

from Jonathan Klos Added 0 0 0

In this video, we look at another word problem that can be represented by a linear system of equations. IN this problem, we are given information about a number of dimes and nickels turned into a coin machine. We are given the total number of coins and the total amount of money the coins were worth and asked to find how many of each coin was turned in. We define our two variables and then write a system that represents the problem. One equation uses the total number of coins, the other equation uses the total value of the coins. We solve this system using substitution, and at the end use the variables to fully answer the question we are given.

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• 07:28

from Jonathan Klos Added 0 0 0

In this video, we look at our methods of determining solutions to a linear system and talk about the strengths of each one. Our methods include graphing, substitution and elimination. Graphing is good to get a quick approximation and to check our work, especially if we use technology. However, to get an exact answer, we need to use substitution or elimination. To determine whether to use substitution or elimination depends on the arrangement of the equations in the system. If one equation already solved for a variable, then substitution would be the most efficient. If both equations are already in standard form, then elimination would be the most efficient.

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• 06:55

from Jonathan Klos Added 0 0 0

In this video, we look at an example of a linear system of equations that has an infinite number of solutions. This is the case of when both equations are really the same equation, and graphically we have one line on top of another line, giving us an infinite number of intersection points, or solutions. We explore the graph and slope-intercept forms of these equations to show they are the same. We then look at what happens when we try to solve the system using the elimination method. When we solve it, the variables cancel each other out and we are left with a true statement such as 0=0. This means that there are an infinite number of solutions.

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• 06:18

from Jonathan Klos Added 0 0 0

In this video, we look at the case of a linear system that has two lines that don't intersect. What this means is that the lines are parallel and that there is no solution to the linear system. There is no point (x,y) such that the values x and y are solutions to both equations. We explore what this looks like graphically, and then we look at what happens when we try to solve the linear system using the substitution method. If there is no solution, what happens is that when solving it, the variables will cancel each other out, and we are left with an false equation.

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• 05:31

from Jonathan Klos Added 0 0 0

In this video, we define what a linear system of equations. A linear system is two or more equations that model the same problem and have the same variables. We often use linear systems when we have a context with two things going on, whether its two cars traveling, two trips to the store, or two pieces of information. Most often when working with linear system, we are very interested in where the two lines intersect graphically. This point is the solution to the system, and represents the x and y variables that make both equations true.

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• 04:05

from Jonathan Klos Added 0 0 0

In this video, we look at how to check if a value is a solution to an inequality. We practice taking a couple of different inequalities and evaluate them at different numbers. One of them ends up true and is a solution. The other one leads to a false statement, so the value is not in the solution set.

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• 06:14

from Jonathan Klos Added 0 0 0

In this video, we look at another example of solving a word problem using a linear inequality. We first define the variable, and the are careful with the wording in the problem to write an inequality that represents the problem. We take the solution set from the inequality to answer the problem.

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• 05:59

from Jonathan Klos Added 0 0 0

In this video we look at a word problem that involves representing the situation with an inequality, and then solving the inequality to solve the problem. The first step is do figure out the question in the problem, and use that to define our unknown variables. After that, we look for key phrases indicating the inequality. We then solve the inequality and answer the problem.

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• 06:27

from Jonathan Klos Added 0 0 0

In this video, we look at solving a more complex inequality. We first need to simplify both sides of the inequality using the distributive property and combining like terms. Then, we add or subtract a variable term to both sides to get only one variable on one side of the inequality. We've now turned it into a two-step equation that we can solve. Once we are done, we check by picking a value in the solution set and testing it in the original inequality.

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