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Algebra I: A Basic Course in Abstract Algebra by Rajendra Kumar Sharma, Sudesh Kumari Shah, Asha Gauri Shankar

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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 x1, x2 …, xn are unknowns (called variables) then a relation of the type

 

a1x1 + a2x2 + : : : + anxn = b      (10.1)

 

where a1, …, an and b are given real constants is called a linear equation in x1,… , xn. The constants a1, …, an are called the coefficients of the variables x1, …, xn respectively. By a solution of equation (10.1) is meant a set of values of x1, …, xn which satisfy it.

Example 10.1.

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

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