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1. Welcome  Name – devANK SHARMA   CLASS – IX A  HOLIDAY HOMEWORK OF MATHS  TOPIC – LINEAR EQUATION IN TWO VARIABLE

2. What is a linear equation in two variable ? Definition : An equation is said to be linear equation in two variables if it is written in the form of ax + by + c=0, where a, b & c are real numbers and the coefficients of x and y, i.e a and b respectively, are not equal to zero.

3. SOME COMMON EXAMPLES OF LINEAR EQUATIONS IN TWO VARIABLES ARE GIVEN ON THE RIGHT SIDE

4. How to solve an linear equation in two variables ? To solve a linear equation in two variables you can follow the given steps Step 1 : Put value for any of the variable (you can put any value for the variable).  Step 2 :  After putting the value you will get valve for the other variable  For better understanding you can see the example on the next slide. 

5. Example  4x + 3y = 12 is a linear equation in two variables If we take x = 0 , then y = ?  4*(0) + 3y = 12  0 + 3y = 12  3y = 12 y = 12/3 y = 4  Therefore, we get that If x = 0 then y will be 4 which can be wrote like (0,4) is the solution or root of equation 4x + 3y = 12 

6. How to plot linear equation on graph We can do so by making a table of solutions of equation . Note : solutions cannot be less than 1 For better understanding you can see the example given

7. In this table the equation is 4x + 3y = 12 first we have found the solution of this equation then we have to plot this on Cartesian graph that we have studied in the previous chapter – 3 Variable Solution Solution X 4 Y 3

8. Now we have  to plot these on the graph as x-coordinate and y-coordinate so they will be (0,4)and(3,0) We can also find the area of the triangle so obtained  In triangle AOB  Area of triangle = ½(B)(H) Where base is 3 and height is 4  So ½(3)(4) = (3)(2) = 6 units square

9. WE CAN PLOT TWO EQUATIONS IN A SINGLE GRAPH BY AGAIN MAKING TABLE OF BOTH EQUATIONS .  FOR EXAMPLE  EQUATION 1 : x + 3y = 6 EQUATION 2 : 2x – 3y = 2 HOW TO PLOT TWO EQUATIONS IN SINGLE GRAPH 

10. Table 1 Equation : x – 3y = 6 Variable  Solution  Solution  Solution  x 6 3 y 1 2 Variable  Solution  Solution  Solution  x 6 3 y -2 -4 Table  Equation : 2x – 3y = 2

11. This is the graphical representation of both the equations  We can also find the area of the triangle obtained  Area of the triangle = ½(B)(H) Where Base = 6 Height = 6 = ½(6)(6) =(3)(6) = 18 units square

12. THANK YOU  Therefore we come to the end of our presentation