The final unit broadens the study of linear equations to situations involving simultaneous equations. Using graphing, substitution, and elimination, students learn to solve systems of equations algebraically and make applications to real-world situations.
Solving Systems of Equations
Analyze and solve linear equations and pairs of simultaneous linear equations.
MGSE8.EE.8 Analyze and solve pairs of simultaneous linear equations (systems of linear equations).
MGSE8.EE.8a 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.
MGSE8.EE.8b 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.
MGSE8.EE.8c 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.