How to solve systems of equations

Systems of Equations

A set of equations with the same variables that can be solved together.

Ways to Solve a System of Equations

Graphing, Substitution, Elimination.

Graphing Method Steps

1. Rewrite equations in slope-intercept form (y = mx + b). 2. Graph the line. 3. Identify solutions.

Intersecting Lines in Graphing

Represents one solution; the point where the lines meet.

Parallel Lines in Graphing

Represents no solution; the lines never touch.

Same Line in Graphing

Represents infinite solutions; all points on the line are solutions.

Slope-Intercept Form

An equation of the form y = mx + b, where m is the slope and b is the y-intercept.

Substitution Method Steps

1. Solve one equation for x or y. 2. Substitute this expression into the other equation. 3. Solve for the remaining variable.

Elimination Method Steps

1. Align equations. 2. Add or subtract to eliminate a variable. 3. Solve for the remaining variable. 4. Substitute back to find the other variable.

No Solution in Systems

Occurs when two lines are parallel, having no points in common.

Infinite Solutions in Systems

Occurs when two equations represent the same line.