The uploaded image outlines the steps for solving systems of inequalities graphically. Here's a summary of the instructions:

1. Write the inequalities in slope-intercept form: Ensure each inequality is written as $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.

2. Use the slope and y-intercept to plot the lines: Use $b$ (the y-intercept) as the starting point, then use $m$ (the slope) to determine the direction and steepness of the line.

3. Draw the line:

   • Use a solid line for inequalities with $\leq$ or $\geq$.
   • Use a dashed line for inequalities with $<$ or $>$.

4. Test a point to determine shading:

   • Choose a point above or below the line, such as $(0, 0)$, if it’s not on the line.
   • Substitute the point into the inequality:
     • If the inequality holds true, shade the side of the line containing the point.
     • If false, shade the opposite side.

5. Systems of inequalities:

   • Follow the above steps for all inequalities in the system.
   • Shade the region where the solutions to the inequalities overlap, as this represents the solution to the system.

Additionally, a tip is provided:

• Flip the inequality sign when dividing or multiplying by a negative number during simplification.

Would you like me to explain any step in detail or solve an example problem for you?

5 Related Questions:

1. How do you find the slope and intercept if the inequality is not in slope-intercept form?
2. What are examples of points to use when testing the shaded region?
3. How do you handle vertical or horizontal lines in systems of inequalities?
4. Can systems of inequalities have no solution? If yes, how can you identify this graphically?
5. What strategies can help simplify inequalities involving fractions?

Tip:

When dealing with complex systems, label each inequality graph on the plot for clarity to easily identify overlapping regions.