Sub-Algebra Topic-Linear equation in two variables Rayat Shikshan Sanstha, Central Region, Satara. Std-9th Sub-Algebra Topic-Linear equation in two variables

Tukaram Hari Wajekar Vidhyalay Funde Rayat Shikshan Sanstha, Raigad Region. Tukaram Hari Wajekar Vidhyalay Funde Std-9th Sub-Algebra Topic-Linear equation in two variables

4 .Linear Equations In Two Veriables. Rayat Shikshan Sanstha, Central Region, Satara. 4 .Linear Equations In Two Veriables. 4.1 - General form of Linear Eqution in Two vesriables. ax + by = c is the general form of linear eqution in two variables x and y were a, b, and real number such that a = 0 , b = 0 , e.g (1) x+2y=5 , (2) 3x – 5y = 2 note that for real numbers a, and b a2 + b2 =0 if and only if a=0 and b= 0 Std-9th Sub-Algebra Topic-Linear equation in two variables

Rayat Shikshan Sanstha, Central Region, Satara. 4.2 . System of linear Eqution in Two Variables Two or more different linear eqution having the same variables taken together form of system of linear equation in two variables. e. g i) 3x- 4y =2; 5x + 3y = 13. ii) 2p + 3q =12 ;4p – 5q =2 Std-9th Sub-Algebra Topic-Linear equation in two variables

4.3 soution system of linear Equtions in two variables Rayat Shikshan Sanstha, Central Region, Satara. 4.3 soution system of linear Equtions in two variables A system of two or more linear equation in two variables(say x and y ) is said a form a system of simulatinuos lineareqution if each question . Std-9th Sub-Algebra Topic-Linear equation in two variables

algebra Rayat Shikshan Sanstha, Central Region, Satara. EXERCISE 4.1 1. Solve the following as per the the given intruction : (i) write any three linear equtions two variables using x and y Ans . x+y =7; 2x – 3y=4; 6y +5y = 11 (ii) Is 7x² + 4y³ =a linear equation two variables justify your answer. Ans. No the given eqution is linear equation, beacause is notof the type ax+by = c Std-9th Sub-Algebra Topic-Linear equation in two variables

Rayat Shikshan Sanstha, Central Region, Satara. 2. Solve the foolowing simultaneous equtions: (i) x+y =4;2x – 5y =1 Solution: x+y =4 2x – 5y =1 Multiply equation (1) by 5, 5x +5y=20 Addingequation(3) and (2), 5x+5y=20 …………..(3) 2x-5y=1 ……………(2) Std-9th Sub-Algebra Topic-Linear equation in two variables

Rayat Shikshan Sanstha, Central Region, Satara. 7x =21 X=21 / 7 x= 3 Substituting x=3 in equation (1) 3+y=4 y=4-3 y =1 Ans. The solution given equation is x =3 and y=1 Std-9th Sub-Algebra Topic-Linear equation in two variables

algebra Rayat Shikshan Sanstha, Central Region, Satara. (II) The method of elimination by substitution: In this method, we find the values of one variables in term of other , from any one of given equation and substitute the values in other equation so, we get a linear equation in one variables. As explained in (I) method of elimation by bequation Std-9th Sub-Algebra Topic-Linear equation in two variables

Topic-Linear equation in two variables EXERCISE Rayat Shikshan Sanstha,Karmaveer Vidyaprabodhini,Madhya vibhag,Satara. Solve-: Solve the following as per the the given intruction : i) If x=1 , y=a is solution of th equation x+3y=10, then find a . ii) Solve the followinng simultaneous equations. a) x+y=4 ; 2x-5y=1 Std-9th Sub-Algebra Topic-Linear equation in two variables

Solve the following simultaneous equation by substitution method : algebra Rayat Shikshan Sanstha, Central Region, Satara. EXERCIZE 4.2 Solve the following simultaneous equation by substitution method : (i) 2x + 3y = -4;x -5y =11 Solution: 2x +3y = -4 ..................(1) x-5y =11 ................(2) Substituting thid value of x in equation(1) 2(5y + 11)+ 3y= -4 10y+22+3y=-4 Std-9th Topic-Linear equation in two variables

Rayat Shikshan Sanstha, Central Region, Satara. 13y= -4 – 22 13y= -26 Y= -26 y=-2 13 Substituting y=-2 in equation (3) X=11+5(-2) x=11-10 X= 1 Ans: The solution of the given equation is x=1 and y=-2 Std-9th Sub-Algebra Topic-Linear equation in two variables

Topic-Linear equation in two variables gylogyat Rayat Shikshan Sanstha,Karmaveer Vidyaprabodhini,Madhya vibhag,Satara. Solve the following simultaneous equations by substitution method. 1)2x + 3y=-4 , x-5y=11 Std-9th Sub-Algebra Topic-Linear equation in two variables

Topic-Linear equation in two variables gylogyat Rayat Shikshan Sanstha,Karmaveer Vidyaprabodhini,Madhya vibhag,Satara. Method of solving particular type of simultane - ous equations -: Consider the simultaneous equations mx +ny = p ; nx+my =q . Here the coefficients of two variables in one equation are inter-changed in the other equation. By adding & subtracting such equations,we can have new equations in the form of x+y = a ; x-y = b which are equivalent to the Std-9th Sub-Algebra Topic-Linear equation in two variables

Topic-Linear equation in two variables gylogyat Rayat Shikshan Sanstha,Karmaveer Vidyaprabodhini,Madhya vibhag,Satara. given equations. These new equations can be solved easily. Exercise 4.3 Questions -: Find the values of (x+y) & (x-y) from the examples given below without solving for x & y : Std-9th Sub-Algebra Topic-Linear equation in two variables

Topic-Linear equation in two variables gylogyat Rayat Shikshan Sanstha,Karmaveer Vidyaprabodhini,Madhya vibhag,Satara. Exercise 1.find the value of x+y from given equations. 1.4x+3y=24 , 3x+4y=25 Q.2 solve the following simultaneous equations 3x+4y=18 , 4x=3y=27 Std-9th Sub-Algebra Topic-Linear equation in two variables

Topic-Linear equation in two variables gylogyat Rayat Shikshan Sanstha,Karmaveer Vidyaprabodhini,Madhya vibhag,Satara. 4x+3y = 24 ; 3x+4y = 25 . 4x +3y = 24 ……………..(1) 3x + 4y = 25 …………….(2) Adding equations (1) & (2) , 7x + 7y = 49 dividing the equations by 7 , x + y = 7 subtracting equation (2) from equation (1) , 4x + 3y = 24 ……………. (1) 3x + 4y = 25 ……………(2) x - y = -1 Std-9th Sub-Algebra Topic-Linear equation in two variables

Topic-Linear equation in two variables gylogyat Rayat Shikshan Sanstha,Karmaveer Vidyaprabodhini,Madhya vibhag,Satara. Answer -: x + y = 7 ; x – y = -1 . Std-9th Sub-Algebra Topic-Linear equation in two variables

Topic-Linear equation in two variables gylogyat Rayat Shikshan Sanstha,Karmaveer Vidyaprabodhini,Madhya vibhag,Satara. 5x + 7y = 17 ; 7x + 5y = 19 . 5x + 7y = 17 ……….(1) 7x + 5y = 19 ……….(2) Adding equations (1) and (2) 12x +12y = 36 dividing the equation by 12 x + y = 3 subtracting equation (1) from (2) 7x + 5y = 17 ……….(2) 5x + 7y = 19 ……….(1) 2x – 2y = 2 Std-9th Sub-Algebra Topic-Linear equation in two variables

Topic-Linear equation in two variables gylogyat Rayat Shikshan Sanstha,Karmaveer Vidyaprabodhini,Madhya vibhag,Satara. dividing the equation by 2 x – y = 1 Answer -: x + y = 3 ; x – y = 1 . Std-9th Sub-Algebra Topic-Linear equation in two variables

Topic-Linear equation in two variables gylogyat Rayat Shikshan Sanstha,Karmaveer Vidyaprabodhini,Madhya vibhag,Satara. Application of simultaneous linear equation in two variables -: Some of the real life problems can be expressed in mathematical form by using linear equations in two variables . Exercise 4.4 Questions -: Frame linear equations in two variables representing the following information : Std-9th Sub-Algebra Topic-Linear equation in two variables

Topic-Linear equation in two variables gylogyat Rayat Shikshan Sanstha,Karmaveer Vidyaprabodhini,Madhya vibhag,Satara. The sum of the is 125 & their difference is 25 . Answer -: Let the numbers be x & y . x > y . The sum of the numbers is 125 . x + y = 125 ……….(1) The difference is 25 . x – y = 25 . ……….(2) Std-9th Sub-Algebra Topic-Linear equation in two variables

Topic-Linear equation in two variables gylogyat Rayat Shikshan Sanstha,Karmaveer Vidyaprabodhini,Madhya vibhag,Satara. ii) The difference between two complementary angle is 6. Answer -: Let the complementary angles be x & y . x > y. Then , x + y = 90 ; x – y = 6. Std-9th Sub-Algebra Topic-Linear equation in two variables

Topic-Linear equation in two variables gylogyat Rayat Shikshan Sanstha,Karmaveer Vidyaprabodhini,Madhya vibhag,Satara. Solve. Two numbers are in the ratio 3:4. If 4 is added to each , the ratio becomes 4:5 find the numbers. Std-9th Sub-Algebra Topic-Linear equation in two variables

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