## Key Concepts

Contents

**To solve a system of linear equations by graphing**- Graph the first equation.
- Graph the second equation on the same rectangular coordinate system.
- Determine whether the lines intersect, are parallel, or are the same line.
- Identify the solution to the system.If the lines intersect, identify the point of intersection. Check to make sure it is a solution to both equations. This is the solution to the system.If the lines are parallel, the system has no solution.If the lines are the same, the system has an infinite number of solutions.
- Check the solution in both equations.

- Determine the number of solutions from the graph of a linear system
- Determine the number of solutions of a linear system by looking at the slopes and intercepts
- Determine the number of solutions and how to classify a system of equations
**Problem Solving Strategy for Systems of Linear Equations****Read**the problem. Make sure all the words and ideas are understood.**Identify**what we are looking for.**Name**what we are looking for. Choose variables to represent those quantities.**Translate**into a system of equations.**Solve**the system of equations using good algebra techniques.**Check**the answer in the problem and make sure it makes sense.**Answer**the question with a complete sentence.

## Glossary

### coincident lines

Coincident lines are lines that have the same slope and same *y*-intercept.

### consistent system

A consistent system of equations is a system of equations with at least one solution.

### dependent equations

Two equations are dependent if all the solutions of one equation are also solutions of the other equation.

### inconsistent system

An inconsistent system of equations is a system of equations with no solution.

### independent equations

Two equations are independent if they have different solutions.

### solutions of a system of equations

Solutions of a system of equations are the values of the variables that make all the equations true. A solution of a system of two linear equations is represented by an ordered pair (*x*, *y*).

### system of linear equations

When two or more linear equations are grouped together, they form a system of linear equations.