Common Core Standards: Math
8. Analyze and solve pairs of simultaneous linear equations.
Dealing with linear equations means knowing how to handle two-variable equations. We don't just have x anymore. We've added a y as well. Why? It makes life interesting. Plus, it's sort of necessary in order to further their mathematical education. Oh yeah, that.
But wait. A pair of linear equations means more than one. So your students should know how to deal with two different linear equations, each with two variables. The goal here is to help your students understand how to handle multiple linear equations and what they mean.
Basically, make sure they don't drown in all the equations and the variables.
- 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.
- 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.
- 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.
- Word Problems and Two Lines
- Verifying Solutions to Systems of Linear Equations
- Solving Systems of Linear Equations by Graphing
- Solving Systems of Linear Equations by Elimination
- Solving Systems of Linear Equations Using Substitution
- Classifying Systems of Linear Equations
- Solving Systems of Linear Equations Using the Addition Method