Solving a system of linear inequalities can be a daunting task for those unfamiliar with the concept. In this article, we will look at the system of linear inequalities of x – 4y < 4 and y < x + 1 and how to interpret the graph of its solution.
Analyzing the System of Linear Inequalities
In order to understand the graph solution to the system of linear inequalities, we must first analyze the system itself. A system of linear inequalities is a set of linear equations that have been combined together. This particular system consists of two equations, x – 4y < 4 and y < x + 1.
To solve a system of linear inequalities, we must find the intersection of the two equations. This is done by plotting the equations on a graph and finding the points where the two lines intersect. This intersection is known as the solution of the system.
Understanding the Graph Solution
Once the two equations have been plotted on a graph, the solution to the system of linear inequalities can be easily seen. The solution is the area of the graph that is shaded in.
In this particular case, the solution is a triangle bounded by the two equations and the x-axis. The triangle is shaded in, indicating that any point within the triangle satisfies both equations. Any point outside of the triangle does not satisfy both equations.
Therefore, the graph of this system of linear inequalities shows the solution to the system. The solution is the area of the graph that is shaded in, which is the triangle bounded by the two equations and the x-axis.
Understanding the solution to a system of linear inequalities can be difficult. However, by plotting the equations on a graph, the solution can be easily seen. In this case, the solution is the triangle bounded by the two equations and the x-axis, which is shaded in. By understanding the graph solution, we can easily identify the solution to the system of linear inequalities.
