 # Systems of Equations (Elimination)

Related Topics:
Common Core for Mathematics
More Math Lessons for Grade 8

Examples, solutions, videos, and lessons to 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.8

### Suggested Learning Targets

• I can identify the solution(s) to a system of two linear equations in two variables as the point(s) of intersection of their graphs.
• I can describe the point(s) of intersection between two lines as the points that satisfy both equations simultaneously.
• I can define "inspection."
• I can solve a system of two equations (linear) in two unknowns algebraically.
• I can identify cases in which a system of two equations in two unknowns has no solution.
• I can identify cases in which a system of two equations in two unknowns has an infinite number of solutions.
• I can solve simple cases of systems of two linear equations in two variables by inspection.
• I can estimate the point(s) of intersection for a system of two equations in two unknowns by graphing the equations.
• I can represent real-world and mathematical problems leading to two linear equations in two variables.
Solving Systems of Equations Algebraically - Opposites Given | 8.EE.C.8b | 8th Grade Math
Example:
Solve using elimination.
-4x + 10y = 20
7x - 10y = 10
Solving Systems Algebraically with Elimination - Perfect Opposites NOT Given | 8.EE.C.8b | 8th Grade Math
Example:
Solve using elimination.
12x + 2y = -4
-5x + y = 20

Solve systems of equations using elimination
1. Multiply one or both of the equations by appropriate numbers so that one of the variables will have the same coefficient with opposite signs.
2. Add the two equations together. Because one of the variables had the same coefficient with opposite signs it will be eliminated when added to the other equation. Solve the resulting equation.
3. Substitute this answer back into one of the original equations to find the value of the remaining variable.
Examples:
1. Solve the system using elimination.
3x + 5y = 4
-2x + 3y = 10
2. Recently Sunset Phone offers two long distance plans. Plan A is \$5.00 per month and \$0.08 a minute. Plan B has no monthly fee but charges \$0.12 a minute. For what number of minutes will the two plans cost the same? Example:
Solve using the elimination (addition) method.
4x - 2y = 16
5x + 2y = 11
Example:
Solve using the elimination (addition) method.
3x + y = -10
7x + 5y = -18
Example:
Solve using the elimination (addition) method.
4x - 2y - 21 = 0
3x = 11 - 8y

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