The graph of the given system of equations represents a visual representation of the solutions to the equations. Specifically, we are dealing with the following two equations:
1. 4x² + 3x + 6 = 0
2. 2x⁴ + 9x³ + 2 = 0
To find the solution set, we need to identify the values of x where the two equations intersect. These intersection points on the graph represent the values of x that satisfy both equations simultaneously.
To approach the problem, we can start by rearranging both equations to form a standard polynomial equation:
4x² + 3x + 6 – (2x⁴ + 9x³ + 2) = 0
Combining like terms, we get:
-2x⁴ – 9x³ + 4x² + 3x + 4 = 0
This is a polynomial equation of degree 4, and solving it will yield the values of x that satisfy both original equations. Depending on the nature of the roots (real or complex), you can find the number of intersection points on the graph.
Graphically, the solution set can be observed at the x-coordinates of the intersection points when you plot the two sides of the equations on a coordinate plane. The y-coordinates of these points will also provide the corresponding outputs for each x-value.
In conclusion, the solution set represented by the graph is determined by finding the intersection points of both curves derived from the two polynomial equations. Each intersection point denotes a solution that satisfies both equations simultaneously.