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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 0 4 Y 0 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 Variabl e Solution Solution Solution x 6 3 0 y 0 1 2 Variable Solution Solution Solution x 6 3 0 y 0 -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