To find the solution set of the given system of equations, we first need to solve for the variable x by equating both expressions:
4x² + 3x – 6 = 2x⁴ + 9x³ + 2x
Rearranging this equation leads us to form a polynomial:
2x⁴ + 9x³ – 4x² + 2x + 6 = 0
This polynomial can be solved for x to find its roots. Each root represents a point where the graphs of the two equations intersect, indicating potential solutions to the system.
Graphically, the solution set is usually represented as the points (x, y) where the two curves meet on the coordinate plane. Analyzing the behavior of the polynomial also provides insights into the nature of these solutions—real or complex, distinct or repeated.
Therefore, the solution set consists of all the x-values that satisfy the equation after finding its roots, along with their corresponding y-values derived from substituting back into either equation.