The Newton-Raphson method works if the equations are differentiable over the domain.
Let f(x) be the non-linear equation and f'(x) by its derivative [with respect to x].
Start with a reasonable guess at the answer, x0.
Then calculate the sequence xn+1 = xn - f(xn)/f'(xn) for n = 0, 1, 2, …
The N-R method should converge to a root.
Ax+By=C
Equations are not linear when they are quadratic equations which are graphed in the form of a parabola
They are not. A vertical line is not a function so all linear equations are not functions. And all functions are not linear equations.
A linear equation is a specific type of function that represents a straight line on a graph. While all linear equations are functions, not all functions are linear equations. Functions can take many forms, including non-linear ones that do not result in a straight line on a graph. Linear equations, on the other hand, follow a specific form (y = mx + b) where the x variable has a coefficient and the equation represents a straight line.
Linear equations are a small minority of functions.
Ax+By=C
In linear algebra, Cramer's rule is an explicit formula for the solution of a system of linear equations with as many equations as unknowns, valid whenever the system has a unique solution.
A system of linear equations is two or more simultaneous linear equations. In mathematics, a system of linear equations (or linear system) is a collection of linear equations involving the same set of variables.
All linear equations are functions but not all functions are linear equations.
There is no quadratic equation that is 'linear'. There are linear equations and quadratic equations. Linear equations are equations in which the degree of the variable is 1, and quadratic equations are those equations in which the degree of the variable is 2.
Equations are not linear when they are quadratic equations which are graphed in the form of a parabola
The answer will depend on what kinds of equations: there are linear equations, polynomials of various orders, algebraic equations, trigonometric equations, exponential ones and logarithmic ones. There are single equations, systems of linear equations, systems of linear and non-linear equations. There are also differential equations which are classified by order and by degree. There are also partial differential equations.
They are not. A vertical line is not a function so all linear equations are not functions. And all functions are not linear equations.
Linear equations are always functions.
A linear equation is a specific type of function that represents a straight line on a graph. While all linear equations are functions, not all functions are linear equations. Functions can take many forms, including non-linear ones that do not result in a straight line on a graph. Linear equations, on the other hand, follow a specific form (y = mx + b) where the x variable has a coefficient and the equation represents a straight line.
Linear equations are a small minority of functions.
Most functions are not like linear equations.