Which equation can be solved by using this system of equations?

the second option 3x³ - 7x² + 5 = 7x⁴ + 2x.

Justification:

Since you have two clearly separated members, you can build a system of equations using each side:

Left side: y = 3x³ - 7x² + 5
Righ side: y = 7x⁴ + 2x.

What advantageous could represent that?

You might, for example, draw the graphs of both functions, y =  3x³ - 7x² + 5 and y = x⁴ + 2x, in the same plane, and the intersection points will be the solutions of the system and, hence, of the original equation.