Elimination
Part of the Graphs & Systems section of Coddy's Algebra journey. Lesson 56 of 64.
Elimination is a way to solve a system by adding or subtracting the equations so that one variable cancels. Add the left sides and the right sides of 2x + y = 7 and x - y = 2. The terms y and -y cancel, and only x is left:
3x = 9
x = 3
Then find y from either equation. The first gives 2(3) + y = 7, so y = 1. The solution is x = 3, y = 1.
Elimination is convenient when the equations are in standard form and one variable has opposite coefficients. Adding the equations cancels those terms.
Challenge
MediumSolve the system x + y = 5; x - y = 1 for x and y.
Try it yourself
Solve for x,y
Test yourselfThis lesson includes a short quiz. Start the lesson to answer it and track your progress.
All lessons in Graphs & Systems
1The Coordinate Plane
Two Numbers, One PointThe Four QuadrantsPoints on the AxesMirror PointsRecap: The Plane4Slope-Intercept Form
y = mx + bThe Starting HeightWrite the EquationSolve for yDraw From Any FormRecap: y = mx + b7Parallel & Perpendicular
Same Slope, Never MeetThe Perpendicular SlopeA Right-Angle LineRecap: Two Relations2From Rule to Line
A Rule Makes PointsThe Points Line UpOn the Line or Not?Between the DotsRecap: Rule to Line5Point-Slope Form
A Point and a SlopeFrom Two PointsFlat or Vertical ThroughDraw From a PointRecap: Point-Slope11Solving Systems Exactly
SubstitutionIsolate FirstEliminationScale, Then AddThree UnknownsTwo Numbers, Two FactsRecap: Two Methods