ALGEBRA

Differences between Simultaneous Linear Equations in Two Variables and Simultaneous Linear Equations in Three Variables.

       

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Simultaneous Linear Equations in Two Variables

Simultaneous Linear Equations in Three Variables

1.

Any first-degree equation containing two variables x and y is called a linear equation in two variables.

Any first-degree equation containing two variables x, y and z is called a linear equation in three variables.

 2.

The general form of linear equation in two variables x and y is ax+by+c = 0, where at least one of a, b is non-zero and a, b, c are real numbers.

The general form of a linear equation in three variables x, y and z is ax+by+cz +d = 0 where a, b, c, d are real numbers, and at least one of a, b, c is non-zero.

3.

A linear equation in two variables of the form ax by c ++ = 0, represents a straight line.

A linear equation in three variables of the form ax by cz d +++= 0, represents a plane.

 

 

Procedure for solving system of linear equations in three variables

 

 

Rational Expressions

 

   Operations of Rational Expressions                                                                                                           

1.     Multiplication of Rational Expressions                                                                         

2.     Division of Rational Expressions

3.     Additions of Rational Expressions

4.      Subtractions of Rational Expressions

 

 

Square Root of Polynomials

 

The following two methods are used to find the square root of a given expression

(i)                           Factorization method

(ii)                         Division method                                                                                                                           

                                                

 

Quadratic Equations

 

Solving a Quadratic Equations

1.     Solving a quadratic equation by factorisation method.                                                                                 

2.     Solving a Quadratic Equation by Completing the Square Method                                                  

3.     Solving a Quadratic Equation by Formula Method

 

 

 

Matrices

 

          Matrix- A matrix is a rectangular array of elements.                                                   

          Rows- The horizontal arrangements are called rows.

          Columns- The vertical arrangements are called columns.

 

Types of Matrices

     

           The following are the different types of matrices                                                                   

1.     Row Matrix

2.     Column Matrix

3.     Square Matrix

4.     Diagonal Matrix

5.     Scalar Matrix

6.     Identity (or) Unit Matrix

7.     Zero matrix (or) null matrix

8.     Transpose of a matrix

9.       Triangular Matrix

 

 

Properties of Matrix Addition and Scalar Multiplication