## 16.1 Outline

- Terminology
- system of equations
- simultaneous solution
- linear system

- Graphing method
- inconsistent system
- dependent system

- Substitution method
- equivalent systems
- procedure

- Linear combination (addition) method
- terminology
- procedure

## 16.1 Essential Ideas

To **solve a system of equations **means to find all replacements of the variables that make all of the equations true at the same time.

The **graphing method** consists of graphing each equation on the same coordinate system and then looking for the point or points of intersection.

The **substitution method** consists of the following steps:

- Solve one of the equations for one of the variables.
- Substitute the expression that you obtain into the other equation.
- Solve the resulting equation.
- Substitute that solution into either of the original equations to find the value

of the other variable. - State the solution.

The **addition method** consists of the following steps:

- Multiply one or both of the equations by a constant or constants so that the coefficients of one of the variables become opposites.
- Add corresponding members of the equations to obtain a new equation in a single variable.
- Solve the derived equation for that variable.
- Substitute the value of the found variable into either of the original equations, and solve for the second variable.
- State the solution.