What defines a system of non-linear equations?

A system of non-linear equations is defined by the presence of at least one equation that is non-linear. This means that the relationships expressed within the equations involve terms that do not form a straight line when graphed, such as quadratic, cubic, or other polynomial terms, exponential functions, logarithmic functions, or trigonometric functions.

When one of the equations in a set is non-linear, it fundamentally alters the approach needed to find solutions, making the system more complex than one composed solely of linear equations. Linear equations can be solved using methods like substitution or elimination, while non-linear equations often require specialized techniques, such as numerical methods, iteration, or graphical analysis, depending on the nature of the non-linearity.

The other options involve more specific conditions that do not accurately characterize non-linear systems. For example, having constant coefficients relates only to linear equations and does not address non-linearity. A collection of linear equations that cannot be solved does not define a non-linear system and may indicate inconsistency or dependency among those equations, but again, does not encompass the definition of non-linearity. Lastly, a system requiring integration methods does not specifically relate to non-linear equations, as certain linear equations can also require such methods depending on the context.