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- 2. MATHEMATICS STANDARD IX Created By Ranjith Nair M C
- 3. NATIONAL ANTHEM Jana-gana-mana-adhinayaka,jaya he Bharata-bhagya-vidhata. Punjab-Sindh-Gujarat-Maratha Dravida-Utkala-Banga Vindhya-Himachala-Yamuna-Ganga Uchchala –Jaladhi-taranga. Tava shubha asisa jage, Tava subha asisa mage, Gahe tava jaya gatha, Jana-gana-mangala-dayaka jaya he Bharata-bhagya-vidhata. Jaya he, jaya he, jaya he, Jaya jaya jaya , jaya he! PLEDGE India is my country. All Indians are my brothers and sisters. I love my country, and I am proud of its rich and varied heritage. I shall always strive to be worthy of it. I shall give respect to my parents, teachers and all elders and treat everyone with courtesy. I pledge my devotion to my country and my people. In their well-being and prosperity alone lies my happiness
- 4. CONTENTS 1.ALGEBRAIC DESCRIPTION 2.OPERATION ON EQUATIONS 3.SUBSTITUTION METHOD 4.ELIMINATION METHOD 5.CROSS MULTIPLICATION METHOD 6.WORD PROBLEMS
- 5. CHAPTER – 6 PAIRS OF EQUATION
- 6. 1.ALGEBRAIC DISCRIPTION You would have used algebra .Suppose we are told this: The perimeter of a rectangle is 20centimetres.Using this fact alone , can we find the length and breadth ? There are many such rectangles . (Can you give some examples?) but since the perimeter is 20cm ,there is a definite relation between the length and breadth . What is it? How do we state this relation in algebraic form? If we denote the length by x and the breadth by y , then 2(x + y) = 20 and simplifying this , we get x + y = 10
- 7. EXAMPLE QUE : Four added to half of a number gives hundred . What is the number? ANS : Let the number be “x” According to the given condition , (1/2 * the number) + 4 = 100 (½ * x) + 4 = 100 x/2 + 4 = 100 x/2 = 100 – 4 x/2 = 96 x = 96 * 2 x = 192
- 8. 2. OPERATION ON EQUATION Every equation says that two numbers are equal . For examples , the meaning of the Equation 2x + 3y = 5 is that on multiplying the number x by 2 , multiplying the number y by 3 and adding the products , we get 5 . So , what do we get on multiplying the number 2x + 3y by 4? 4 * 5 = 20 ,right? That is , 8x + 12y = 20 Thus multiplying the numbers on either side of any equation by the same number , we get another equation ; and this new equation would be true for all numbers for which the original equation is true. Again , for any two numbers x and y for which both the equations 2x + 3y = 5 4x - 5y = 7 are true , we would have
- 9. 3.SUBSTITUTION METHOD In the method , we first find the value of one variable (y) in terms of another variable (x) from one equation . Substitute this value of y in the second equation . Second equation becomes a linear equation in x only and it can be solved for x. Putting the value of x in the first equation , we can find the value of y. This method of solving a system of linear equation is known s the METHOD OF ELIMINATION BY SUBSTITUTION . ‘Elimination’ because we rid of y or ‘eliminate’ y from the second equation. ‘Subtsitution’ because we ‘substitute the value of y in the second equation.
- 10. 4.ELIMINATION METHOD In elimination method , we eliminate one of the Unknown quantites by using the following steps 1. The given equations are multiplied by a suitable number so that the coefficients of one of the variables become numerically equal’ 2. If the numerically equal coefficients are opposite in sign then add the new Equation , otherwise subtract them. 3. Solve the resulting linear equation to get the value of one of the variables. 4. Substitute this value in any of the given equation and get the value of the other variable.
- 11. 5.CROSS MULTIPLICATION METHOD By method of elimination by substitution , only those equation can be solved . But the method of cross multiplication discussed below is applicable in all the cases ; whether the system has a unique solution , no solution no solution or infinitely many solutions.
- 12. 6.WORD PROBLEMS We have already learnt how to solve a pair of linear Equations . Now , we will discuss to solve situational problems (word problems) On the daily life . Here first of all we have to form a linear pair of equations according To given conditions in the problem . Then , we will solve the pair of linear equations Formed .
- 13. THANK YOU
Editor's Notes
- #3: MA