What is liner equation
Answers
Step-by-step explanation:
an equation between two variables that gives a straight line when plotted on a graph
{\displaystyle a_{1}x_{1}+\cdots +a_{n}x_{n}+b=0,}
where {\displaystyle x_{1},\ldots ,x_{n}} x_{1},\ldots ,x_{n} are the variables (or unknowns), and {\displaystyle b,a_{1},\ldots ,a_{n}} {\displaystyle b,a_{1},\ldots ,a_{n}} are the coefficients, which are often real numbers. The coefficients may be considered as parameters of the equation, and may be arbitrary expressions, provided they do not contain any of the variables. To yield a meaningful equation, the coefficients {\displaystyle a_{1},\ldots ,a_{n}} a_1, \ldots, a_n are required to not all be zero.
Alternatively a linear equation can be obtained by equating to zero a linear polynomial over some field, from which the coefficients are taken.
The solutions of such an equation are the values that, when substituted for the unknowns, make the equality true.
In the case of just one variable, there is exactly one solution (provided that {\displaystyle a_{1}\neq 0} {\displaystyle a_{1}\neq 0}). Often, the term linear equation refers implicitly to this particular case, in which the variable is sensibly called the unknown.