Figure 2: Which graph shows a mixed-degree system with only one solution? The solution to the system in question is in the section R. This section represents all solutions to the system. Both the inequalities can have the same solution in this section.
Figure 2
The equation for a mixed-degree system has a solution. A solution is a smooth curve on an x-y plane with a vertical axis labeled x and a horizontal axis labeled y. The curve begins below the x-axis at the origin and rises to its highest point above the y-axis at a point on the left. Then, the curve descends and ends at a point above the x-axis.
Figure 2 shows a mixed-degree system. In this example, the first equation in the system is multiplied by two to eliminate y. Then, the two equations are added side-by-side. The result is 2 comma negative two, the solution of the given system.
The graphs of two equations in a mixed-degree system will be the same if the axes are parallel. For example, if y = -six x plus eight, then the graphs of the two lines will meet at point three. If the two graphs intersect, then there is one solution.
X yplane
An X yplane graph shows x versus y, the x-axis labeled with the origin and y-axis labeled with the slope, and the point of intersection between the two lines. The slope, f, of the mixed-degree system can be seen as a curve that begins at the left x-axis and moves downward. The solution to the system is a point on the y-axis.
When the X yplane graph shows two solutions of the same inequality, it is a mixed-degree system. A system that has exactly one solution has an X-yplane graph with two points that lie outside the solution region. In the following graph, point B and point N are the solutions of y = x + 1 and x – y = p.
Scatterplot
The scatterplot for a mixed-degree system consists of two parts. The region above the dashed line is labeled section Q, and the region below it is labeled section P, R, and S. The region above the dashed line represents the solutions to the system. The region below the dashed line represents the solutions to both inequalities.
If we draw the scatterplot using the x-axis, we can observe that the data points are symmetric with respect to the vertical line. The left half of the cluster starts with data points that have y coordinates greater than 10. The right half of the cluster extends upward and to the right.
We can plot two categorical variables in a scatterplot using geom_count(). The code in this section uses functions from a later section. Geom_count() and geom_tile() are functions similar to scatterplot but they use a color scale to show the number of observations for each point.
Scatterplots are useful for displaying relationships between variables. However, they do not necessarily indicate causality. The observed relationship may be a result of a third factor or just a coincidence. Therefore, it is important to understand the differences between the variables and use them to your advantage.
The scatterplot is useful for illustrating complex problems. It can also help you to see where a problem is located. The x-yplane is divided into four regions. In the right region, a dashed line passes through the yaxis at a point above the x-axis. The dashed line then intersects the solid line at a point on the left side of the x-axis.
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