## Linear Systems With Two Variables (FORMING EQUATION)

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• ### Nihar H

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LEAR TO FORM EQUATION WITH TWO VARIABLES

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Part-I free.notebook February 01, 2016 PAIR OF LINEAR EQUATION IN TWO VARIABLES Obtain the linear equation in two variables from the following information Father tells his son, "five years ago, I was seven times as old as you were. After five years, I will be three times as old as you were" Suppose present age of father is x years Suppose present age of Son is y years Age of father and son before five years Age of father = x — 5 Age of son = y— 5 x 5+35 7y x— 7 y + 30 After five years Age of father — Age of son x 5 3y x 3y Nil-IAR SIR AHMEDABAD 15 15 10 35 3y+ 15 May 23-10:33 (i) (2) 1
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Part-I free.notebook February 01, 2016 Father tells his son, "ten years ago, I was six times as old as you were. After five years, I will be four times as old as you were" Suppose present age of father is x years Suppose present age of Son is y years Age of father and son before ten years Age of father Age of son x— 10 x 10 x — 10 + 60 — 6y After five years x —10 Y 10 6 (y 10) 6y — 60 0 Age of father Age of son x 4y+5 Nil-IAR SIR AHMEDABAD 20 20 15 4y+ 20 0 0 May 23-12:36 (2) 2
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Part-I free.notebook February 01, 2016 Father tells his son, "fifteen years ago, I was seven times as old as you were. After ten years, I will be four times as old as you were". Suppose present age of father is x years Suppose present age of Son is y years Age of father and son before fifteen years Age of father Age of son x 15 x— 15 x —15 Y 15 17 (y 15) 7y 105 x— 15+ 105 —7y -O x 7)' + 90 = 0 After ten years Age of father Age of son X 10 x X 10 X 10 4y 40 4y 30 X + 10 Y + 10 4y + 40 May 23-12:49 (1) (2) Nil-IAR SIR AHMEDABAD 3
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Part-I free.notebook February 01, 2016 The total weight of father and son is 70kg and the weight of son is one sixth of the weight of his father. Suppose 'weight of Father is x Suppose weight of son is y The total weight of father and son is 70kg x + y — 70 (1) The weight of son is one sixth of the weight of his father. x x — 6y 0 (2) May 30-08:09 Nil-IAR SIR AHMEDABAD 4
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Part-I free.notebook February 01, 2016 Thesumofthecostof1kgappleand1kgpine-appleisRs.150. Costoflkgappleisfourtimesthecostoflkgpine-apple. Suppose cost of Ikg pineapple is x Rupees Suppose cost of Ikg apple is y Rupees The sum of the cost of 1 kg apple and Ikg pine apple is Rs. 150 x + Y 150 (1) The cost of 1 kg apple is twice the cost of 1 kg pine apple. Pine apple Apple 0 May 23-12:58 (2) Nil-IAR SIR AHMEDABAD 5
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Part-I free.notebook The sum of the cost of Ikg apple and Ikg pine-apple is February 01, 2016 Rs.150. Cost of Ikg apple is four times the cost of Ikg pine — apple. Suppose cost of Ikg pineapple is x Rupees Suppose cost of Ikg apple is y Rupees The sum of the cost of 1 kg apple and Ikg pine apple is Rs. 150 x+y 150 (1) The cost of 1 kg apple is Four times the cost of 1 kg pine apple. Pine apple 4x Nil-IAR SIR AHMEDABAD Apple 0 May 23-13:15 (2) 6
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Part-I free.notebook February 01, 2016 Nin got twice the marks obtained by Nihar in the annual exam of 10 th. The sum of the marks obtained by them is 135. Suppose Nitin got x marks Suppose Nihar got y marks The sum of the marks obtained by them is 135 x + y — 135 (1) Nitin got twice the marks obtained by Nihar x 2y—0 Nil-IAR SIR AHMEDABAD (2) May 23-13:25 7
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Part-I free.notebook February 01, 2016 Nitin got thrice the marks obtained by Nihar in the annual exam of 10th. The sum of the marks obtained by them is 150. Suppose Nitin got x marks Suppose Nihar got y marks The sum of the marks obtained by them is 150 x+y— 150 (1) Nitin got thrice the marks obtained by Nihar (2) May 23-13:29 Nil-IAR SIR AHMEDABAD 8
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Part-I free.notebook February 01, 2016 The ages oftwo girls are in the ration of 5:7. Eight years ago,their ages were in the ration of 7:13. Suppose present age of one girl is x years And other girl is of Y years The ages oftwo girls are in the rationof 5:7 Y .. 7x—5y 7 (1) their ages Eight years ago one girl x — 8 Second gir y — 8 Eight years ago,their ages were in the ration of 7:13. 13x 13(x 8) 13x 104 7y 104+56 13x 7y 48 13x- 7y 7 13 7y — 56 48 May 30-10:57 (2) Nil-IAR SIR AHMEDABAD 9
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Part-I free.notebook The sum and difference of the reciprocals of the ages of a son and father are 3 respectively— & 40 • 40 Suppose age of the father is x years February 01, 2016 Age of son is' y ' years reciprocal of father's age reciprocal of Son's age 1 x 1 The sum of the reciprocals of the ages of father and son is 5 40 1 1 1 1 y 5 40 3 40 (1) (2) May 30-11:33 Nil-IAR SIR AHMEDABAD 10
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Part-I free.notebook February 01, 2016 The sum of two positive numbers is 25. Five times of the smaller number is 5 more than three time of larger number. Suppose smaller positive number is x Larger positive integer is y The sum of two positive numbers is 25 x = 25 Five times of the smaller number is 5 more than three time of larger number. 5x 5 5 (2) May 30-11:46 Nil-IAR SIR AHMEDABAD 11
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Part-I free.notebook Raj got 2 times the marks as obtained by Nil in the annual examination of math. The sumof their marks is 140. Suppose Raj obtained x marks And Nil obtained y marks The sumoftheir marks is 140 February 01, 2016 x — 140 (1) Raj got- times the marks as obtained by Nil in the annual examination of math. x x 3 4 4 4x 4x Nil-IAR SIR AHMEDABAD (2) May 30-12:05 12
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Part-I free.notebook February 01, 2016 The total cost of 7 pens and 5 pencils is Rs.50 and the total cost of 5 pens and 7 pencils is Rs.46. Suppose cost of one pen is Rs. x and cost of one pencil is Rs. Y Cost of 7 pen is and cost of 5 pencils is 5y The total cost of 7 pens and 5 pencils is Rs.50 7x +5y—50 total cost of 5 pens and 7 pencils is Rs.46. (1) 5x + 7y — 46 Nil-IAR SIR AHMEDABAD (2) May 30-12:20 13
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Part-I free.notebook 3y—5 February 01, 2016 Length of a rectangle is five less than the thrice of its breadth. The perimeter of the rectangle is 110. Suppose length of a rectangle is x Suppose Breadth of a rectangle is y The perimeter of the rectangle is 110. x x 2(x+y x + y — 55 110 110 55) (1) Length of a rectangle is five less than the thrice of its breadth. x 0 (2) May 23-13:34 Nil-IAR SIR AHMEDABAD 14
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Part-I free.notebook February 01, 2016 Length of a rectangle is five less than the thrice of its breadth. The perimeter of the rectangle is 110. Suppose length of a rectangle is x Suppose Breadth of a rectangle is Y x + x — 110 110 — 55 x x (1) Length of a rectangle is ten less than the Four time of its breadth x + 10 Nil-IAR SIR AHMEDABAD 10 (2) May 23-18:11 15
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Part-I free.notebook February 01, 2016 1 The sunn af the weights af a father and a son is 85 kg, The weight af the san is - of the weight of his father Suppose Father's weight is x kg Son's weight is y kg The sum of the weights of a father and a son is 85 kg x 85 The weight of the son is - of the weight of his father x x x 4y 4 4y 4y O (2) (2) May 23-19:32 Nil-IAR SIR AHMEDABAD 4 16
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Part-I free.notebook February 01, 2016 The sum of the weights of a father and a son is 85 kg. The weight of the son is half of the weight of his father Suppose Father's weight is x kg Son's weight is Y kg The sum of the weights of a father and a son is 85 kg x + y — 85 The weight of the son is half of the weight of his father x X x 2 x 2y (2) (2) May 23-19:42 Nil-IAR SIR AHMEDABAD 17
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Part-I free.notebook x— 3y February 01, 2016 In a cricket match Sachin Tendulkar score thrice the sehwag's score . Both of them together make a total score of 200 Runs. Suppose sachin tendulkar score is x runs And Sehwag score Y runs Both of them together make a total score of 200 Runs. x+y— 200 (1) Sachin Tendulkar score thrice the sehwag' s score O Nil-IAR SIR AHMEDABAD (2) May 23-19:45 18
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Part-I free.notebook February 01, 2016 In a cricket match Sachin Tendulkar score twice the sehwag's score . Both of them together make a total score of 300 Runs. Suppose sachin tendulkar score is x runs And Sehwag score Y runs Both of them together make a total score of 300 Runs. x y — 300 (1) Sachin Tendulkar score twice the sehwag' s score Sachin sehwag 0 (2) May 23-20:40 Nil-IAR SIR AHMEDABAD 19
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Part-I free.notebook February 01, 2016 Rakesh purchase 15 pens and 20 pencils. He has to pay Rs.190 for it. The sum ofthe cost ofa pen and pencil is Rs.11. Obtain a pair of linear equation from the given data. Suppose cost of a pen is Rs.x and cost of a pencil is The sum of the cost of a pen and pencil is Rs.11. x + y — 11 Cost of 15 pens —15x Cost of 20 pencils 20y Cost of 15 pens and 20 pencils is Rs. 190 (1) 15x+ 20y- 190 Nil-IAR SIR AHMEDABAD (2) May 23-21:01 20
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Part-I free.notebook February 01, 2016 A shopekeeper sells 5 pants and 8 shirst for Rs.3100, the cost ofa pair of pant and a shirt is Rs.500. Suppose cost of apant is Rs. The cost of a pair of pant and a shirt is Rs.500. x+y— 500 cost of 5 pants — 5x costof8 shirts= 8y (1) x Cost of 5 pants and 8 shirts is Rs.3100 5x +8y —3100 Nil-IAR SIR AHMEDABAD (2) May 23-22:18 21
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Part-I free.notebook February 01, 2016 In tossing a balanced coin the probabilityof getting a head on its face is twice to the probbalityof getting a tail on its face. The sum of both the probabilities (head and tail) is 1 Suppose probablity of getting head on the face of coin is x And the probability of getting tail on the face of coin is y The sum of both the probabilities (head and tail) is 1 (1) the probabilityofgetting a head on its face is twice to the probbalityof getting a tail on its face x Nil-IAR SIR AHMEDABAD (2) May 23-22•.27 22
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Part-I free.notebook February 01 , 2016 When we draw a graph, If both the straight line intersects at a common point then it has Unique (only one) Soluon. If both the lines are parallel, it does not intersect at any pointthen it has no soluon. If both the line idencal or coincide, then it has infinitely many soluons. 5 4 3 2 1 -5 4 -3 -2 -1 0 1 2 3 4 5 6 1 2 3 May 24-11 : 06 NIHAR SIRAHMEDABAD 23
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Part-I free. notebook February 01 , 2016 Solve the followinglinearequation and showit onthe graph. 工 十 2 = 5 & 3 ェ 十 5 = 13 3 光 十 5 = 13 3 ェ = 13 ー 5 ア x 十 2 = 5 13- ら X 3 x = 5 ー 2 メ Ta れ 0 ア = 2 亡 0 れ = 2 3 t 佖 れ ア = 1 3 13- ら 第 % = 5 ー 2 ァ = 5 ー 2 ア 3 x = 5 ー 2 ( 1 ) = 5 ー 2 ( 2 ) 13-5 ( 2 ) 3 x = 5 ー 2 x = 5 ー 4 13-10 3 工 3 1 1 2 T 佖 た ⅲ ア = 5 13-2 ら 3 13- ら X 3 -12 3 13- ら ( 引 3 Y 000000000 を 0000000000 ロ 000 ロ 0000 を ロ ロ 000 ロ ロ 000 ロ ロ 00 ロ 0 ロ 00 置 ロ ロ ロ 00 ロ ロ 000 000000000 ロ ロ 000 ロ 0000 000000000 第 0000000000 0 ロ 00 ロ 0 ロ 00 第 ロ ロ ロ 00 ロ ロ 000 000000000 ■ 0000000000 000000000 新 0000000000 000000000 0000000000 0 ロ 00 ロ 0 ロ 000 ロ ロ ロ 00 ロ ロ 000 000000000 羆 0000000000 000000000 0000000000 000000000 0000000000 0000 ロ 00000 ロ ロ 000 ロ ロ 000 000000000 眠 0000000000 00000g0000000000000 X Y' The 5 社 れ 0 れ set of 亡 ん e paw of れ e 佖 r eq 社 れ 0 れ な ( May 24-11 : 12 NIHAR SIRAHMEDABAD 24
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Part-I free. notebook February 01 , 2016 3 % 十 4 = 15 3 工 十 4 ァ = 10 & 3x 十 4 ァ = 15 4 ァ = 15 ー 3 光 4 ァ = 10 ー 3x 1 ら -3 10-3 4 4 t 佖 れ 光 = 6 亡 れ 0 工 = 1 光 = 5 ta れ 0 = 2 1 ら -3 ェ 10-3 ェ 1 ら -3 ア ア 10-3 : て 4 4 4 4 15-3 ( 印 10-3 ( 6 ) 1 ら -3 ( 1 ) 10-3 ( 2 ) 4 4 4 4 10-18 15-15 1 ら -3 10-6 4 4 4 4 0 - 4 0 12 4 4 1 5 6 2 X 3 0 1 Y -1 0 X There れ 0 50 巨 0 れ of 肱 を eq 社 佖 れ 0 れ May 24-12 : 30 NIHAR SIRAHMEDABAD 25

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