Which Graph Shows the Solution to the System of Linear Inequalities? X – 4Y < 4 Y < X + 1
The graph should depict a shaded area in the coordinate plane. When graphing the system of linear inequalities X – 4Y < 4 and Y < X + 1, it is important to understand the relationship between the two inequalities and how they intersect.
By representing these relationships graphically, we can visualize the solution set and gain a deeper understanding of the feasible region. This visual representation aids in identifying the values of X and Y that meet the criteria of both inequalities. In the context of real-world applications, such as optimization and resource allocation problems, graphing the solution to a system of linear inequalities provides valuable insights into feasible solutions. Additionally, graphing offers a clear and concise way to communicate the solutions to others.
Graphing Linear Inequalities
Graphing inequalities on the coordinate plane allows us to visually represent the solution to a system of linear inequalities. In this case, we are given two inequalities: X – 4Y < 4 and Y < X + 1. To graph these inequalities, we follow a few steps.
Step 1: Graph the boundary lines for each inequality. To do this, we rewrite the inequalities as equations and graph the corresponding lines.
Step 2: Choose a test point not on the boundary line. Substitute the coordinates of this point back into the original inequality.
Step 3: Shade the region that satisfies the inequality. If the test point satisfies the inequality, shade the region containing the point; otherwise, shade the opposite region.
By following these steps, we can determine which graph displays the solution to the system of linear inequalities. Remember to correctly label the axes and any intercepts along the way.
Conclusion
Based on the graphs presented, we can conclude that the solution to the system of linear inequalities X – 4Y < 4 and Y < X + 1 lies in the shaded region where the two graphs intersect. The region represents the set of values that satisfy both inequalities simultaneously.
By analyzing the graphs carefully, we can determine the range of possible solutions for this system of linear inequalities.