LEARN 3 EASY Ways to Determine the Number of Solutions to a System | 8.EE.C.8 💗

In this video math lesson we will learn how to determine the number of solutions to a system of linear equations in three ways. We will learn how to determine from a graph of a system of linear equations if the number of solutions is one, none, or infinitely many. We will discover that when the two line intersect there is one solution, if the two lines are parallel there is no solution, and if the lines are the same or coincide there are infinitely many solutions. The second way we will learn to determine the number of solutions is by solving using substitution or elimination. If you solve and have one x and one y value there is one solution or point of intersection. If you eliminate both variables while solving and are left with a true numerical equation, then there are infinitely many solutions. If the numerical statement is false, then there are no solutions. The third way we will learn is to consider the system in slope-intercept form. If the slopes are different, there is one solution. If the slopes are the same and the y-intercepts are different, then there is no solution. Lines with the same slope and different y-intercepts are parallel and will never intersect. If the slopes and the y-intercepts are the same, then there are infinitely many solutions since they are the same line. Student practice problems are embedded in the lesson with modeled exemplar solutions.

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00:00 Introduction
00:34 The 3 Types of Solutions - Graphing
02:16 Student Practice #1
03:48 Student Practice #2
04:48 Types of Solutions - Algebraically
06:38 Student Practice #3
08:28 Student Practice #4
09:35 Student Practice #5
10:52 Determine # of Solutions Using y=mx+b
13:01 Student Practice #6
14:13 Student Practice #7
14:48 Student Practice #8
15:17 Student Practice #9

Common Core Math Standards
Analyze and solve pairs of simultaneous linear equations.
8.EE.C.8.A Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously.
8.EE.C.8.B Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection. For example, 3x + 2y = 5 and 3x + 2y = 6 have no solution because 3x + 2y cannot simultaneously be 5 and 6.