rayat shikshan sanstha, central region, satara. topic-linear equation in two variables sub-algebra...

Rayat Shikshan Sanstha, Central Region, Satara.

Topic-Linear equation in two variables

Sub-Algebra

Std-9th

Rayat Shikshan Sanstha Maharaja Sayajirao

Vidhyalaya ,Satara


Sub-Algebra


Std-9th


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


Sub-Algebra

Std-9th


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


Sub-Algebra

Std-9th


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 .


Sub-Algebra

Std-9th

algebra


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 Topic-Linear equation in

two variables Sub-

AlgebraStd-9th


2. Solve the foolowing simultaneous equtions: (i) x+y =4;2x – 5y =1Solution: x+y =4 2x – 5y =1Multiply equation (1) by 5, 5x +5y=20Addingequation(3) and (2),5x+5y=20 …………..(3)2x-5y=1 ……………(2)


Sub-Algebra

Std-9th


7x =21X=21 / 7 x= 3Substituting x=3 in equation (1)3+y=4 y=4-3 y =1Ans. The solution given equation is x =3 and y=1


Sub-Algebra

Std-9th

algebra


(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


Sub-Algebra

Std-9th

EXERCISE

Rayat Shikshan Sanstha,Karmaveer Vidyaprabodhini,Madhya vibhag,Satara.

Std-9th Sub-Algebra


Solve-:1. 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

algebra


EXERCIZE 4.21. 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


13y= -4 – 22 13y= -26 Y= -26 y=-2 13 Substituting y=-2 in equation (3) X=11+5(-2) x=11-10 X= 1Ans: The solution of the given equation is x=1 and

y=-2


Sub-Algebra

Std-9th

gylogyat


Std-9th Sub-Algebra


Solve the following simultaneous equations by substitution method. 1)2x + 3y=-4 , x-5y=11

gylogyat


Std-9th Sub-Algebra


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

gylogyat


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


gylogyat


Std-9th Sub-Algebra


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

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i) 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


Sub-Algebra

Std-9th

gylogyat


Answer -: x + y = 7 ; x – y = -1 .


Sub-Algebra

Std-9th

gylogyat


ii) 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


Sub-Algebra

Std-9th

gylogyat


dividing the equation by 2 x – y = 1 Answer -: x + y = 3 ; x – y = 1 .


Sub-Algebra

Std-9th

gylogyat


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 :


Sub-Algebra

Std-9th

gylogyat


i) 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)


Sub-Algebra

Std-9th

gylogyat


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.


Sub-Algebra

Std-9th

gylogyat


Solve. Two numbers are in the ratio 3:4. If 4 is added to each , the ratio becomes 4:5 find the numbers.


Sub-Algebra

Std-9th

THANKS FOR ATTENTION

rayat shikshan sanstha, central region, satara. topic-linear equation in two variables sub-algebra...

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