These lessons, with videos, examples, and solutions, help Grade 8 students learn how to analyze and solve pairs of simultaneous linear equations.
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.
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.
C. Solve real-world and mathematical problems leading to two linear equations in two variables. For example, given coordinates for two pairs of points, determine whether the line through the first pair of points intersects the line through the second pair.
Common Core: 8.EE.8ab
The following table shows examples of solving systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations.
Solving Systems of Linear Equations (8.EE.8)
Graphing - 3 possibilities:
One solution, No solution and Infinite solutions.
Solve using the substitution method.
Solve using the elimination method.
Using Systems of Linear Equations (8.EE.8)
Types of solutions for systems of equations
This video discusses the characteristics of solutions of linear equations that have one solution, no solutions, or an infinite number of solutions.
Three main types of solutions of linear equations with examples
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