Elimination Method in Linear Systems

Substitution

Graphing

Elimination

Matrix Method

When both equations are solved for Y

When one equation is solved for a variable

When equations have opposite coefficients

When graphing is not possible

Solve for one variable

Graph the equations

Make coefficients of one variable opposite

Substitute one equation into another

The equations become identical

The variable is eliminated

The coefficients double

The solution is found

By dividing the equations

By subtracting the equations

By multiplying one or both equations

By adding a constant

Add a constant to one equation

Use substitution instead

Graph the equations

Multiply the equations to create opposite coefficients

Fractions are easier to calculate

Decimals are always rounded

Fractions are exact and not rounded

Decimals are less common

By checking the coefficients

By graphing the solution

By substituting the solution back into the original equations

By using a calculator

A graph of the system

A new equation with one variable

An equation with no variables

A solution to the system

Using a calculator

Graphing or substitution

Rewriting the equations

Guessing the solution