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Within the lesson, students are provided with two sets of equations with two unknowns. These sets of equations can be solved algebraically for a total of four solutions. Solving the systems is straightforward and simply involves adding or subtracting to one side from the other side to find an equation that matches. I am going over how to solve a system of two equations with two unknowns using algebra. Solving a system is straightforward and simply involves adding or subtracting to one side from the other side to find an equation that matches. The ideas and skills discussed in the lesson can be used for classes that range from 3rd grade through 8th grade. The title of this homework is "Lesson 8 Homework Practice Solve Systems Of Equations Algebraically". However, I am going to begin at the beginning when I say that when solving a system of equations, it is very important to try to find the solutions in terms of x before doing so algebraically. This will help you in your understanding of how algebra works with actual practice problems. I have two sets of equations with two unknowns in each set. These equations can be solved algebraically for four possible solutions. The first set is: And the second is: Making substitutions for x and y, I get the following equations. Now, I need to solve these systems algebraically. These two equations can be solved using elimination of variables. I will subtract the second equation from the first equation to get an equation with only one variable that will be x. Since there is only one variable, there can only be one solution for this problem. This means that when I find the solution for x in this second system, it will also be a solution of the first system of equations thus giving me two solutions in total. I do the same thing to get the following equation. Now I am going to solve this second system of equations. I can do this by just adding or subtracting from one side of the equation to the other side. So adding these two equations together, I get: or: x - y = 7 There is more than one solution to a system of equations if you have multiple variables in your equations. For example, I have two more systems of systems with two unknowns each that you can see here. In these systems, there are two unknown variables so their total number of solutions is four. Here are the equations for this second system of systems: And here are the equations for this third system of systems: The key idea in the lesson is to use algebra to find a solution to a system. You can do this by adding or subtracting from one side of an equation on the other side to get a new equation. From there, you can solve it algebraically. There is more than one solution to a sytem if you have multiple variables in your equations. For example, I have two more systems of systems with two unknowns each that you can see here. In these systems, there are two unknown variables so their total number of solutions is four. cfa1e77820
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