LINEAR EQUATIONS IN TWO VARIABLES (CONCEPT )

 1. Linear equation in two variables : An equation which contains two variables and the degree of each term containing variable is one.

• ax + by + c = 0 is the general form of a linear equation in two variables

2. Simultaneous linear equations : Two linear equations in two variables at the same time, they are called simultaneous equations.

• 5x - 3y = 8; 3x + y = 2

3. Graph of a linear equation in two variables : Steps to follow for drawing a graph of linear equation in two variables

1. Find at least 4 ordered pairs for given equation


2. Draw X- axis, Y-axis on graph paper and plot the points


3. See that all 4 points lie on one line


4. Note the co-ordinates of the point of intersection of the two graphs.

4. Determinant :

    

        |a  b|

        |c  d|

• Determinant represents a number which is (ad-bc)


• (ad-bc) is the value of determinant

4. Determinant : Using determinants, simultaneous equaions can be solved easily and in less space. This method is known as determinant method. Steps to follow

1. Write given equations in the form ax + by = c


2. Find the values of determinants D, Dx and Dy


3. Using, x = D_x/D  and   y = D_y/D,   find values of x, y.