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Elimination

Part of the Graphs & Systems section of Coddy's Algebra journey. Lesson 53 of 61.

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 $2\cdot 3+y = 7$ , 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

Medium

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

Try it yourself

x+y = 5

x-y = 1

Find $x$ , $y$

All lessons in Graphs & Systems

1Points and Rules

Two Numbers, One Point A Rule Makes Points The Points Line Up

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

2The Whole Plane

The Four Quadrants Mirror Points On the Line or Not?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