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### Math Assignment Class X Ch-3 | Linear Equations in Two Variables

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** CHAPTER 3
CLASS X**

__PAIR OF LINEAR EQUATIONS IN TWO VARIABLE__

**Extra questions of chapter 3 class 10 : Pair of Linear Equations in Two Variable with answer and hints . Useful math assignment for the students of class 10**

**Basic points of Chapter 3 Pair of Linear Equations in two variable.**

**ASSIGNMENT BASED ON CH-3 CLASS 10**

**Question 1**

**By comparing the ratios of the coefficients find the nature of sol./ graph / consistency or inconsistency**

**a) 2x - 3y = 1 ; x + 2y = 2**

**Ans: Unique solution, intersecting lines, consistent**

**b) 3x - y = 6 ; 6x - 2y = 4**

**Ans: No solution, parallel lines, inconsistent**

**c) x + 3y = 8 ; 2x - 3y = 12**

**Ans: Unique solution, intersecting lines, consistent**

**d) 9x + 3y + 12 = 0 ; 18x + 6y = - 24**

**Ans: Many solution, coincident lines, consistent**

**e) 6x - 3y +10 = 0 ; 2x – y + 9 = 0**

**Ans: No solution, parallel lines, inconsistent**

**Question 2)**

**Find the value of p so that the following equations have coincident lines**

**a) 2x + y - 5 = 0; 6x + 3y + p = 0 ****Ans [p = -15]**

**b) x + 2y + 7 = 0; 2x + py + 14 = 0**

**Ans [p = 4]**

**c) 3x + 4y + 2 = 0; 9x + 12y + p = 0 Ans[p = 6]**

**d) x + 5y - 7 = 0 ; 4x + 20y + p = 0**

**Ans [p = -28]**

**Question 3) Find k if the following equations are inconsistent**

**a) 8x + 5y = 9; kx + 10y = 15 Ans: k =16**

**b) (3k + 1)x + 3y - 2 = 0; (k**

^{2 }+ 1)x + (k - 2)y - 5 = 0**c) 3x + y = 1; (2k - 1)x + (k - 1)y = 2k + 1**

**d) kx + 3y = k – 3; 12x + ky = k**

**Answer: a) **** k = 16 , b) k = -1, c) k = 2, d) k = 土 6**

**Question 4) Find a & b or k so that the following equations have infinitely many solutions**

**a) (a + b)x - 2by = 5a + 2b + 1; 3x - y = 14 ****Ans [a = 5, b = 1]**

**b) 2x - 3y = 7; (a + b)x + (a + b)y = 4a + b ****Ans [-5, -1]**

**c) (2a - 1)x + 3y – 5 = 0; 3x + (b - 1)y – 2 = 0 ****Ans [a = 17/4, b= 11/5]**

**d) kx + 3y = 2k + 1; 2(k + 1)x + 9y = 7k + 1 ****Ans [k = 2]**

**e) 2x + 3y = 7; (k – 1)x + (k + 2)y = 3k ****Ans [k = 7]**

**Question 5) Solve the following equations graphically**

**a) x + y = 3; 2x + 5y = 12 ****Ans [1, 2]**

**b) 2x + 3y + 5 = 0; 3x - 2y - 12 = 0 ****Ans [2, -3]**

**PROBLEMS BASED ON GRAPHICAL METHOD**

**Question 6**

**Solve the following equations graphically. Shade the area between lines and x-axis. Also find the area of the shaded triangle.**

**a) x + y = 5; 2x - y = - 2 **

**[Sol. (1, 4) & Area= 12]**

**b) x - y + 1 = 0; 3x + 2y - 12 = 0**

** ****[Area= 7.5]**

**c) 2x + y = 6; 2x - y + 2 = 0**

**[Area= 8]**

**Question 7)**

**Solve 2(x - 1) = y & x + 3y = 15 graphically and find the coordinates where lines meet the y-axis. Also shade the triangle between the lines and y-axis.**

**Ans [(3, 4), (0, -2), (0, 5)]**

**Question 8)**

**Solve x – y = 1 & 2x + y = 8 graphically and shade the area between the lines and the y-axis. Also find the area of the triangle.**

**Ans [Area = 13.5]**

**SOLVE THE PAIR OF LINEAR EQUATIONS BY**

**ALGEBRAIC METHOD**

**Question 9)**

**Solve the following pair of linear equations in two variables**

**a) x + y = 7 ; 3x - 2y = 1 ****Ans [3, 4]**

**b) 3x + 2y = 10 ; 4x - y = 6**

**Ans [2, 2]**

**c) Ans [2, -3]**

**d) 2x + y – 35 = 0 ; 3x + 4y - 65 = 0**

**Ans [15, 5]**

**e) x/a - y/b = 0 ; bx + ay = 4ab**

**Ans[2a, 2b]**

**f) - 6x + 5y = 2 ; - 5x + 6y = 9 Ans[3, 4]**

**g) 23x - 29y = 98 ; 29x - 23y = 110**

**Ans [3, - 1]**

**h) 99x + 101y = 499 ; 101x + 99y = 501**

**Ans [x = 3, y = 2]**

**i) a(x + y) + b(x - y) = a**

^{2 }– ab + b^{2};**a(x + y) - b(x - y) = a**

^{2 }+ ab + b^{2 }**j) ax + by = a - b ;**

**bx - ay = a + b**

**Ans [1, - 1]**

**PROBLEMS BASED ON DAILY LIFE SITUATIONS**

**Question 10) Find two numbers whose sum is 75 and difference is 15**

**Ans [45 and 30]**

**Question 11) Sum of two numbers is 8. Find the numbers if sum of their reciprocal is 8/15.**

**Question 12)**

**The ratio of incomes of two persons is 9 : 7 and the ratio of their expenditure is 4 : 3 If each of them saves Rs 200/ month, find their monthly incomes.**

**Ans [Rs1800 & Rs 1400]**

**Question 13**

**If 2 is subtracted from the numerator and 1 is added to the denominator, a fraction becomes 1/2 , but when 4 is added to the numerator and 3 is subtracted from the denominator , it becomes 3/2. Find the fractions.**

**Ans [8/11]**

**Question 14)**

**37 pens and 53 pencils together cost Rs 320, while 53 pens and 37 pencils together cost Rs 400. Find the cost of a pen and that of a pencil.**

**Ans [Rs 6.50 and Rs 1.50]**

**Question 15)**

**In a two digit number , the ten’s digit is three times the unit’s digit. When the number is decreased by 54, the digits are reversed. Find the number.**

**Ans [93]**

**Question 16)**

**The sum of the two digit number and the number obtained by reversing the order of its digits is 121, and the two digits are differ by 3. Find the numbers.**

**Ans [47 or 74]**

**Question 17)**

**The sum of a two digit number and the number formed by interchanging the digits is 110. If 10 is subtracted from the first number , the new number is 4 more than 5 times the sum of the digits in the first number. Find the first number**

**Ans [64] **

**Question 18)**

**A fraction is such that if the numerator is multiplied by 3 and the denominator is reduced by 3, we get 18/11, but if the numerator is increased by 8 and the denominator is doubled , we get 2/5. Find the fraction.**

**Ans [12/25]**

**Question 19)**

**The denominator of a fraction is 4 more than twice the numerator. When both the numerator and denominator are decreased by 6, then the denominator becomes 12 times the numerator. Find the fraction**

**Ans [7/18]**

**Question 20)**

**If twice the son’s age in years is added to the fathers age, the sum is 70. But if twice the father’s age is added to the son’s age, the sum is 95. Find the age of father and son. Ans [40, 15]**

**Question 21)**

**Two years ago, a father was 5 times as old as his son. Two years later , his age will be 8 more than 3 times the age of his son. Find the present ages of father and son.**

**Ans [42, 10] **

**Question: 22**

**Sum of two
numbers is 105 and their difference is 45. Find the numbers.**

**Answer:
Required Numbers are: 75, 30**

**Question: 23**

**Three years
ago, Rashmi was thrice as old as Nazma. Ten years later, Rashmi will be twice
as old as Nazma. How old are Rashmi and Nazma now ?**

**Solution Hint**

**Let present
age of Rashmi and Nazma be x years and y years respectively**

**Therefore, x
- 3 = 3(y - 3)**

**Or x - 3y +
6 = 0**

**And x + 10 =
2(y + 10)**

**Or x – 2y –
10 = 0**

**Solving
equations to get x = 42, y = 16**

**Present age
of Rashmi is 42 years and that of Nazma is 16 Years**

**Question 24**

**Tara scored 40 marks in a test getting 3 marks for each right answer and losing 1 mark for each wrong answer. Had 4 marks been awarded for each correct answer and 2 marks been deducted for each wrong answer, then Tara would have scored 50 marks. Assuming that Tara attempted all questions, find the total number of questions in the test.**

**Solution Hint**

**Let number
of correct answers be x and**

**number of
incorrect answers be y**

**3x - y = 40**

**4x - 2y = 50**

**Solving, we
get x = 15, y = 5**

**Total number
of questions = 20**

**HIGHER ORDER THINKING SKILL (HOTS)**

**(Deleted from CBSE syllabus)**

Question 1)

Question 1)

**Ans: x = 2, y = 1]**

Question 2)

Question 2)

**Ans: x = 1, y = 1**

Question 3)

Question 3)

Ans: x = 8, y = 3

Ans: x = 8, y = 3

**4) ax + by = c ; bx + ay = 1 + c**

**5) ax + by = c ; bx - ay = 0**

**6) 6(ax + by) = 3a + 2b ; 6(bx + ay) = 3b + 2a**

**Ans [1/2, 1/3]**

**7) ax + by = a**

^{2 }+ b^{2}; bx - ay = 0 Ans [a, b]**8) (a - b)x + (a + b)y = a**

^{2 }- 2ab - b^{2 }; (a + b)(x + y) = a^{2 }+ b^{2 }** **

**9) 2(ax - by) + (a + 4b) = 0 ;**

^{ }**2(bx + ay) + (b - 4a) = 0**

**Ans [-1/2, 2]**

**10) x**

**+ y = 5xy ; 3x + 2y = 13xy**

**Ans [x = 1/2 , y = 1/3]**

**11)**

**Q12) A person can row downstream 20km in 2 hours. And upstream 4km in 2 hours. Find the speed of boat in still water and that of the current.**

**Ans [6,4]**

**Q13) A boat covers 32 km upstream and 36 km downstream in 7 hours. Also it covers 40 km upstream and 48 km downstream in 9 hours. Find the speed of the boat in still water and that of the stream.**

**Ans [10 km/h and 2 km/h]**

**THANKS FOR YOUR VISIT**

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### Comments

Good collections

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