Question

What is meant by consistent? What is meant by inconsistent?

Answer 1

Hint: In this question, you should remember the concepts of geometry such as consistent and inconsistent as we know generally consistent means continues and inconsistent means in-continues you can use this information to bring out the answer to the question.

Complete step-by-step solution -
In mathematics and particularly in algebra a linear or nonlinear equation system is called Consistent. Where there is at least one set of unknown values that satisfy each equation in the system, that is, every equation remains true as an identity when replaced in each of the equations. In comparison, if there is no set of values for the unknown that satisfies all the equations, a linear or nonlinear equation structure is considered inconsistent Or we can say that two or more equations that can be solved using one set of variables are consistent. An example of the equation of consistency is $4x-y=1$ and $-8x+2y=4$.

Note: You would be aware of that the linear and nonlinear equations are the algebraic concepts which can be explained as a linear equation which is an algebraic equation which consists of a term has an exponent in each term thus the representation of the equation graphically results in a straight line for example $ax + by + c = 0$. Whereas a nonlinear equation says that the equation which has more than 2 variables are called nonlinear equations or the equation which cannot be represented in the form of $ax + by + c = 0$ is a nonlinear equation for example $y=x^2$.