Elimination

Part of the Graphs & Systems section of Coddy's Algebra journey. Lesson 54 of 64.

Two equations may also be ADDED, side to side, and the sum is another true equation. When opposite terms meet, a variable vanishes. In 2x + y = 7; x - y = 2 the y terms are opposites, so adding the equations kills y at once:

3x = 9

x = 3

and y follows from either line: 2(3) + y = 7 gives y = 1. This is elimination: add (or subtract) the equations so one variable cancels.

Elimination shines when the equations sit in standard form: no isolating at all, just one addition aimed at the cancelling pair.

Challenge

Solve the system x + y = 5; x - y = 1 for x and y.

Try it yourself

x + y = 5x - y = 1

Solve for x,y

Test yourself

This 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 Point The Four Quadrants Points on the Axes Mirror Points Recap: The Plane

4Slope-Intercept Form

y = mx + b The Starting Height Write the Equation Solve for y Draw From Any Form Recap: y = mx + b

7Parallel & Perpendicular

Same Slope, Never Meet The Perpendicular Slope A Right-Angle Line Recap: Two Relations

10Systems by Graphing

Two Lines, One Answer Solve by Drawing Check the Crossing When Lines Never Cross Recap: By Graphing

2From Rule to Line

A Rule Makes Points The Points Line Up On the Line or Not?Between the Dots Recap: Rule to Line

5Point-Slope Form

A Point and a Slope From Two Points Flat or Vertical Through Draw From a Point Recap: Point-Slope

8Function Notation

The Name of a Rule Inputs With Signs Find the Input The Graph of f Recap: f(x)

11Solving Systems Exactly

Substitution Isolate FirstEliminationScale, Then Add Three Unknowns Two Numbers, Two Facts Recap: Two Methods