## Objective:

**To solve systems of linear equations by graphing.**

## Vocabulary:

**System of Equations**- two equations with the same variables that are solved simultaneously.

## Notes:

Steps to graph linear inequalities on a coordinate plane.- Graph each line on the same coordinate plane.
- The point of intersection of the two lines is the solution.
- Check the solution in both equations.

## Examples:

### Find the solution by graphing the system of equations.

Since these equations are written in standard form I will graph by finding the intercepts. (See section 4.3 for help.)

1st equation:

- When x is 0, y must be −3. This gives me the point (0, −3).
- When y is 0, x must be 21/4 or 5¼. This is the point (5¼, 0).
- Plot the points and draw the line.

2nd equation:

- When x is 0, y must be −3. This gives me the point (0, −3).
- When y is 0, x must be −9/11. This gives the point (−9/11, 0).
- Plot the points and draw the line.

The point of intersection of the two lines is the solution. The solution of this system appears to be (0, −3). Check it in both equations to verify that it is the solution.

Since these equations are written in slope-intercept form I will graph by plotting the y-intercept and using the slope. (See section 4.5 for help.)

1st equation:

- The y-intercept is 4. Plot it.
- The slope is 2, rise 2 and run right 1 to find another point.
- Draw the line.

2nd equation:

- The y-intercept is 1. Plot it.
- The slope is −½; go down 1 and run right 2 to find another point.
- Draw the line.

The point of intersection of the two lines is the solution. The solution of this system appears to be (2, 0). Check it in both equations to verify that it is the solution.