What do you do to graph (and shade) a system that does overlap?
To graph and shade a system that overlaps, such as a system of linear equations or inequalities, follow these steps:
1. Identify the equations or inequalities in the system: Write down each equation or inequality given in the problem. For example, a system of linear equations might look like:
Equation 1: 2x + y ≤ 6
Equation 2: x + 3y > 9
2. Graph each equation or inequality separately: Treat each equation or inequality as a separate line or region on the graph. To graph a linear equation, convert it to slope-intercept form (y = mx + b) and plot the y-intercept (b) and use the slope (m) to find additional points on the line. To graph an inequality, treat it as either a solid line (≤ or ≥) or a dashed line (< or >), depending on whether or not it includes the points on the line itself.
3. Determine the overlapping region: On the graph, identify the region where the lines or shaded regions intersect or overlap. This is the solution to the system.
4. Shade the overlapping region: Determine whether the overlap region should be shaded or not. If the system includes inequality symbols (≤, ≥, <, or >), you need to shade the overlapping region to indicate the solution set. You may use a different shading style, such as diagonal lines or shading with a specific color, for clarity.
5. Label the solution: If required, label the overlapping region with an appropriate notation to indicate the solution set. For example, you might write "Solution Set" or "S" next to the shaded region.
Remember, if the system contains equations (without inequality symbols), the solution is the point(s) where the lines intersect. If the system contains inequalities, the solution is the overlapping area that satisfies all the given inequalities.