## Chapter 10

## System of Linear Equations

An equation of the type *ax = b*, where *a* and *b* are real constants and *x* is an unknown, is called a linear equation in *x*. If *x _{1}, x_{2} …, x_{n}* are unknowns (called variables) then a relation of the type

*a*(10.1)

_{1}x_{1}+ a_{2}x_{2}+ : : : + a_{n}x_{n}= b

where *a _{1}, …, a_{n}* and

*b*are given real constants is called a linear equation in

*x*. The constants

_{1},… , x_{n}*a*are called the coefficients of the variables

_{1}, …, a_{n}*x*respectively. By a solution of equation (10.1) is meant a set of values of

_{1}, …, x_{n}*x*which satisfy it.

_{1}, …, x_{n}**Example 10.1.**

- 3
*x*–0.2*y*= 5*is a linear equation in two variables x and y. x*= 1,*y*= –10*is a solution. More solutions also exist*. -
*is a linear equation in three variables x, y, z. x*= 0,*y*= 3,*z*= 0 ...

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