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Calee Leger - 8th Grade Math
email: [email protected]
11/18-11/21
Unit 3 Lesson 13
Solving Systems Algebraically: Substitution and Elimination
LEARNING OBJECTIVE:
Students will be able to solve systems of two linear equations with two variables algebraically using substitution and elimination methods and interpret the solution as the point of intersection of the two lines.
- Systems of two linear equations in two variables can have one solution (intersecting lines), no solution (parallel lines), or infinitely many solutions (same line). The algebraic solution corresponds to the coordinates of the intersection point.
- Substitution method: solve one equation for one variable and substitute into the other; best when an equation already has a variable isolated or can be easily isolated.
- Elimination method: add or subtract equations (possibly after multiplying one or both equations by constants) to eliminate a variable; best when coefficients are easily made opposites.
- Always check solutions by substituting the found values into both original equations to verify correctness.
- Common vocabulary: system of equations, substitution, elimination, solution, consistent, inconsistent, dependent, independent.
Louisiana 8.EE.C.8 — Analyze and solve pairs of simultaneous linear equations.
Louisiana 8.EE.C.8 — Understand that solutions to a system correspond to points of intersection of their graphs and classify systems as one solution, infinitely many solutions, or no solution.
- An ordered pair (x,y) is a solution to a system of two linear equations if substituting x and y into both equations makes both equations true; graphically this corresponds to a point that lies on both lines.