Choosing the Right Method for Solving Linear Equations

A graphical representation of equations

Two linear equations with the same two variables

A single linear equation

A set of quadratic equations

Only one method is actually useful

To confuse students

To ensure accuracy of the solution

To apply the most efficient method based on the equation's form

The system has infinitely many solutions

The lines are perpendicular

The system has no solution

The system has one unique solution

No solution

Cannot be determined

One unique solution

Infinitely many solutions

The lines intersect at one point

The lines are parallel

The lines are perpendicular

The lines overlap completely

Graphing

None of the above

Substitution

Elimination

By identifying the intersection point of the lines

By determining the y-intercept of each line

By calculating the slope of each line

By finding the area under the curve

When equations are in standard form

When one equation is already solved for one variable

When equations have no solution

When coefficients are multiples of each other

All variables have the same coefficient

Coefficients of one variable are opposites or multiples

One variable is easily isolated

Equations are in slope-intercept form

Some methods are more accurate than others

Graphing is only useful for simple equations

All methods will lead to the same solution

Substitution is always the preferred method