Question

State whether the given equation is linear or not.Also, state the no. of variables in the equation \[2x+1+2=0\]

Answer 1

Hint:Polynomials are the algebraic expressions which consist of variables and coefficients. Variables are also sometimes called indeterminate. We can perform the arithmetic operations such as addition, subtraction, multiplication and also positive integer exponents for polynomial expressions but not division by variable.


Complete step by step solution:
Degree of a Polynomial:
The degree of a polynomial is defined as the highest degree of a monomial within a polynomial. Thus, a polynomial equation having one variable which has the largest exponent is called a degree of the polynomial.
A polynomial is defined as an expression which contains two or more algebraic terms. It is made up of two terms, namely Poly (meaning “many”) and Nominal (meaning “terms.”). Polynomials are composed of:
Constants. Example: 1, 2, 3, etc.
Variables. Example: g, h, x, y, etc.
Exponents: Example: 5 in x5 etc.

Linear equation: an equation between two variables that gives a straight line when plotted on a graph is called linear equation.
Given;
\[2x+1+2=0\]
It is a linear equation in which no. of variables is 1 and no, of constants is 2.
Formula of linear equation, when one variable is given is \[Ax+B+C=0\]
Formula of linear equation, when two variables are given is \[Ax+By+C=0\]

Note: The standard form for linear equation in two variables\[Ax+By=C\] is a linear equation in standard form, when an equation is given in this form; it is pretty easy to find both intercepts\[(x\,and\,y)\]. This form is also very useful when solving systems of two linear equations.