CBSE Class 10 Mathematics Pair Of Linear Equations In 2 Variables Worksheet Set H

1. Solve graphically the system of linear equations: x + 3y = 11, 3x + 2y = 12 (3, 5)

2. Draw the graph of the equation x – y + 1 = 0 and 3x + 2y – 12 = 0. Determine the coordinates of the vertices of the triangle Formed by these lines and the x – axis, and shade the triangular region (-1, 0), (2, 3) and (4, 0)

3. Check graphically whether the pair of linear equations 4x – y – 8 = 0 and 2x – 3y + 6 = 0 is consistent. Also find the vertices of the triangle formed by these lines with the x - axis

4. Solve: a) x y = 1 , x y = 1

x + y 5 x – y 7 (x = -1, y = 1/6)

b) 149x – 330y = - 511, - 330x + 149y = - 32 (x=1, y=2)

c) 37x + 43y = 123, 43x + 37y = 117 (x=1, y=2)

d) (a – b) x + (a + b) y = a2 – 2ab – b2 , (a + b) x + (a + b) y = a2 + b2 (x = a +b, y = - 2ab/a +b)

e) a x – by = a2 + b2 , x – y = 2b ( a + b , a – b)

f) ax + by = a – b , bx – ay = a + b (x -1, y = -1)

g) 10 + 2 = 4 , 15 - 5 = - 2 (x = 3, y = 2)

x + y x - y x+ y x - y

h) x + y = a + b, x + y = 2 (a2, b2)

a b a2 b2

5. Find the value(s) of k for which the pair of linear equations k x + 3y = k – 2 and 12x + k y = k has no solution (k = ±6)

6. Find the value of k, for which the pair of equations 3x + 5y = 0, k x + 10y = 0, has a non zero solution (k = 6)

7. Find the value of a and b for which the system of equation has infinitely many solutions:

a) 2x + 3y = 7, (a – b) x + (a +b) y = 3a +b – 2 (5, 1)

8. Find the value of k, for which the given linear pair has a unique solution: 2x + 3y – 5 = 0, k x – 6y -8 = 0 (k ≠ -4)

9. 10 students of class x took part in mathematics quiz. If the number of girls is 4 more than the number of boys, find the number of boys and number of girls who took part in the quiz. (3, 7)

10. The larger of the two supplementary angles exceeds the smaller by 18 degrees. Find the angles (99˚, 81˚)

11. In a two digit number, the sum of the digits is 9. If the digits are reversed, the number is increased by 9. Find the number (45)

12. The sum of digits of a two digit numbers is 7. If the digits are reversed, the new number decreased by 2 equals twice the original Number.Find the number (25)

13. A fraction becomes 4/5 if 1 is added to both the numerator and the denominator. However, if 5 is subtracted from both numerator and the denominator the fraction becomes ½. Find the fraction (7/9)

14. Two years ago, a father was five times as old as his son. Two years later, his age will be 8 more than three times the age of the son. Find the present ages of father and son (10, 42)

15 90% and 97% pure acid solutions and mixed to obtain 21 litres of 95% pure acid solution. Find the amount of each Type of acid to be mixed to form the mixture (x=6, y=15)

16. 2 women and 5 men can together finished a piece of work in 4 days, while 3 women and 6 men can finis h it in 3 days. Find the time taken by 1 woman alone to finish the work, and that taken by 1 man alone. (18, 36)

17. A boat goes 16km upstream and 24km downstream in 6hrs. It can go 12km up and 36km down in the same time. Find the speed of the boat in still water and the speed of the stream. (8, 4)

18. Students of a class are made to stand in rows. If 4 students are extra in a row , their would be 2 rows less. If 4 students are less in a row, there would be 4 more rows. Find the number of students in the class. (96)

19. The perimeter of a rectangle is 44 cm. If its length is increased by 4 cm and its breadth is increased by 2cm, its area is increased by 72 sqcm. Find the dimensions of the rectangle. (12, 8)

20. The sum of two numbers is 1000 and the difference between their squares is 256000. Find the numbers (628, 372)

21. If (x + 2) is a factor of x3 + ax2 + 4bx + 12 and a + b = - 4, find the values of a and b (-3, -1)

22. Two numbers are in the ratio 3: 4 and if 4 are added to each, the ratio becomes 4:5. Find the numbers (12, 16)

23. The ratio of incomes of two persons is 9: 7 and the ratio of their expenditures is 4 : 3. If each of them saves Rs. 200 per Month, find their monthly expenditures. (Rs1800, Rs1400)

24. Sum of the areas of two squares is 468m2.If the difference of their perimeter is 24m, find the sides of two square (18, 12)

25. A boy travels for x hrs at 8km/hr and then for y hrs at 7km/hr. If he goes 37km altogether in 5hrs, find x and y (2, 3)

26. Places A and B are 100km apart on a highway. One car starts from A and another from B at the same time. If the cars travel in The same direction at different speeds, they meet in 5 hrs. If they travel towards each other they meet in 1 hour. What are the Speeds of the two cars

1. Solve graphically the system of linear equations: a) x + 3y = 11, 3x + 2y = 12 (3, 5)

2. Draw the graph of the equation x – y + 1 = 0 and 3x + 2y – 12 = 0. Determine the coordinates of the vertices of the triangle

Formed by these lines and the x – axis, and shade the triangular region (-1, 0), (2, 3) and (4, 0)

3. Solve: a) xy = 1 , xy = 1

x + y 5 x – y 7 (x = -1, y = 1/6)

b) 149x – 330y = - 511, - 330x + 149y = - 32 (x=1, y=2)

c) 37x + 43y = 123, 43x + 37y = 117 (x=1, y=2)

d) (a – b) x + (a + b) y = a2 – 2ab – b2 , (a + b) x + (a + b) y = a2 + b2 (x = a+b, y = - 2ab/a+b)

e) ax – by = a2 + b2 , x – y = 2b

f) 10 + 2 = 4 , 15 - 5 = - 2 (x = 3, y = 2)

x+ y x-y x+ y x - y

g) x + y = a + b, x + y = 2 (a2, b2)

a b a2 b2

4. Find the value(s) of k for which the pair of linear equations kx + 3y = k – 2 and 12x + ky = k has no solution (k = ±6)

5. Find the value of k, for which the pair of equations 3x + 5y = 0, kx + 10y = 0, has a non zero solution (k = 6)

6. Find the value of a and b for which the system of equation has infinitely many solutions:

a) 2x + 3y = 7, (a – b) x + (a +b) y = 3a +b – 2 (5, 1)

7. Find the value of k, for which the given linear pair has a unique solution: 2x + 3y – 5 = 0, kx – 6y -8 = 0 (k ≠ -4)

8. 10 students of class x took part in mathematics quiz. If the number of girls is 4 more than the number of boys, find the number of boys and number of girls who took part in the quiz. (3, 7)

9. The larger of the two supplementary angles exceeds the smaller by 18 degrees. Find the angles (99˚, 81˚)

10. In a two digit number, the sum of the digits is 9. If the digits are reversed, the number is increased by 9. Find the Number (45)

11. A fraction becomes 4/5 if 1 is added to both the numerator and the denominator. However, if 5 is subtracted from Both the numerator and the denominator the fraction becomes ½. Find the fraction (7/9)

12. Two years ago, a father was five times as old as his son. Two years later, his age will be 8 more than three times the age of the son. Find the present ages of father and son (10, 42)

13 90% and 97% pure acid solutions and mixed to obtain 21 litres of 95% pure acid solution. Find the amount of each Type of acid to be mixed to form the mixture (x=6, y=15)

14. 2 women and 5 men can together finished a piece of work in 4 days, while 3 women and 6 men can finis h it in 3 days. Find the time taken by 1 woman alone to finish the work, and that taken by 1 man alone. (18, 36)

15. A boat goes 16km upstream and 24km downstream in 6hrs. It can go 12km up and 36km down in the same time. Find the speed of the boat in still water and the speed of the stream. (8, 4)

16. Students of a class are made to stand in rows. If 4 students are extra in a row , their would be 2 rows less. If 4 students are less in a row, there would be 4 more rows. Find the number of students

17. The perimeter of a rectangle is 44 cm. If its length is increased by 4 cm and its breadth is increased by 2cm, its area is increased by 72 sqcm. Find the dimensions of the rectangle.

18. The sum of two numbers is 1000 and the difference between their squares is 256000. Find the numbers (266,744)

19. If (x + 2) is a factor of x3 + ax2 + 4bx + 12 and a + b = - 4, find the values of a and b (-3, -1)

20. Two numbers are in the ratio 3: 4 and if 4 are added to each, the ratio becomes 4:5. Find the numbers (12, 16)

21. Solve by the method of cross multiplication:

(a – b) x + (a + b) y = a² – 2ab – b², (a + b)(x+y) = a² + b² (a+b, -2ab/a+b)

22. The ratio of incomes of two persons is 9: 7 and the ratio of their expenditures is 4 : 3. If each of them saves Rs. 200 per Month, find their monthly expenditures. (Rs1800, Rs1400)

23. Sum of the areas of two squares is 468m2.If the difference of their perimeter is 24m, find the sides of two square

24. Rohan travels 600km from his home partly by train and partly by car. He takes eight hours if he travels 120km by train And rest by car. He takes 20min more if he travels 200km by train and rest by car. Find the speed of train and car. (60km/hr, 80km/hr)

25. A boy travels for x hrs at 8km/hr and then for y hrs at 7km/hr. If he goes 37km altogether in 5hrs, find x and y (2, 3)

Q.- Determine graphically the co-ordinates of the vertices of the triangle, the equations of whose sides are: y=x,3y=x, x+y=8

Explanation: y = x

Ans- d. intersect only at a point or they coincide with each other

Explanation: A system of two linear equations in two variables is consistent, if their graphs intersect only at a point, because it has a unique solution or they may coincide with each other giving infinite solutions.

LINEAR EQUATIONS IN TWO VARIABLES

Q.- Half the perimeter of a rectangular garden, whose length is 4 m more than its width, is 36 m. find the dimensions of the garden. 

 More Question-

1) Find four solutions of the linear equation 5x – 4y = - 8

2) Find two solutions of the linear equation 2(x + 3) – 3(y + 1) = 0

3) Draw the graph of the linear equation 2x + 3y = 12. At what points the graph of the equation Cuts the x axis and the y axis

4) Draw the graphs of the equations x + y = 6 and 2x + 3y = 16on the same graph paper. Find the coordinates of the points where the two lines intersect

5) The auto rickshaw fare in a city is charged Rs 10 for the first km and Rs 4 per km for Subsequent distance covered. Write the linear equation to express the above statement Draw the graph of the linear equation

6) Check whether the graph of the linear equation 2x +3y = 12 passes through the point (1, 3)

7) If (2, 5) is a solution of the equation 2x + 3y = m, find the value of m (m= 19)

8) Frame a linear equations in the form ax + by + c = 0 by using the given values of a, b and c

a) a= -2, b =3, c= 4 b) a = 5, b= 0, c= -1

9) Find the value of k, if x = 2, y = 1 is a solution of the equation 2x + 3y = k (k = 7)

10) Give the geometric representation of (A) 3 x + 9 =0 as an equation in (a) one variable

(B) 2x +1= x - 4 (b) Two variable

11) Solve the equation 2x + 1 = x – 3 and represent the solution on the number line

12) Give the equation of two lines passing through (2, 14). How many more such lines are there and Why

13) Solve for x: a) (3 x + 2) / 7 + 4 (x + 1) / 5 = 2/3 (2x + 1) (x=4)
b) 8y + 21/4 = 3y + 7 (y = 7/20)

14) If present ages of son and father are expressed by x and y respectively and after ten years father Will be twice as old as his son. Write the relation between x and y

15) Does point (1, 3) lie on the line 3y = 2x + 8

16) If (2, 3) and (4, 0) lie on the graph of equation ax + by = 1. Find value of a and b.Plot the graph the equation obtained

17) Express the equation y = 2x + 3 in the standard form and find two solutions. Is (2, 3) it’s Solution?

18) Express y in terms of x from the equation 3x + 2y = 8 and check whether the points (4, -2) lies on the line.

19) write each of the following as an equation in two variables (in standard form):
(a) X = - 5 (b) y = 2 (c) 2x = 3 (d) 5y = 2

Pair of Linear Equations in Two Variables

More Question-

1.The solution of the system of equation and is √2x + √5y = 0 and √3x - √7y = 0 is 
(A) x = √3, y = √5
(B) x = √2, y = √7
(C) x = 1, y = √2
(D) x = 0, y = 0

2.If a pair of values x, y satisfies an equation, then x and y are called _____ of equation.

3.The ratio between a two-digit number and the sum of digits of that number is 4 : 1. If the digit in the unit place is 3 more than the digit in the tenth place, what is that number ?
(A) 63
(B) 36
(C) 24
(D) None of these.

4.If the ratio of boys to girls in a class is B and the ratio of girls to boys is G, then B + G is
(A) greater than 1 or equal to 1
(B) greater than 1
(C) less than 1
(D) equal to 1

5.The income of P and Q are in the ratio 3 : 2 and expenses are in the ratio of 5 : 3. If both saveRs 200, What is the income of P ?
(A) Rs 700
(B) Rs 1000
(C) Rs 1200
(D) None of these.

6.Which of the following system of equations has no solution?
(A) 3x + y = 2, 9x + 3y = 6
(B) 4x - 7y + 28 = 0, 5y - 7x + 9 = 0
(C) 3x - 5y - 11 = 0, 6x - 10y - 7 = 0
(D) None of these.

7.The LCM of two numbers is 630 and their HCF is 9. If the sum of the numbers is 153, their difference is
(A) 72
(B) 27
(C) 81
(D) 18

8.For the equations 5x - 6y = 2 and 10x = 12y + 7
(A) there is no solution
(B) there exists unique solution
(C) there are two solutions
(D) there are infinite number of solutions.

9. For what value of p does the system of equations 2x - py = 0, 3x + 4y = has nonzero solution?
(A) p = - 6
(B) p = (-8/3)
(C) p = (-2/3)
(D) p = -(3/8)

10.The sum of the digits of a two digits number is 8. If the digits are reversed, the number is decreased by 54. Find the number.
(A) 35
(B) 17
(C) 71
(D) 53.

11.For what value of p will the system of equations 3x + y = 1, (2p - 1)x + (p- 1)y = (2P + 1) has no solution?
(A) p = 2
(B) p ≠ 2
(C) p = - 2
(D) p ≠ - 2

12.For what value of k, the system of equations x + 2y = 3, 5x + ky + 7 = 0 has unique solution?
(A) k = 10
(B) All real values except 10
(C) All natural numbers except 10
(D) None of these.

13.For what value of k, the system of equations kx - y = 2, 6x - 2y = 3 has infinitely many solutions?
(A) k = 3
(B) k ≠ 4
(C) k = 6
(D) Does not exist.

14.For what values of a and b will the equations 2x + 3y = 7, (a - b)x + (a + b)y = (3a + b - 2) represent coincident lines?
(A) a = 5, b = - 1
(B) a = 5, b = 1
(C) a = -5, b = - 1
(D) a = 5, b = - 1

15.Divide 62 into two parts such that fourth part of the first and two-fifth part of the second are in the ratio 2 : 3.
(A) 24, 38
(B) 32, 30
(C) 16, 32
(D) 40, 22

16.37 pens and 53 pencils together cost Rs320, while 53 pens and 37 pencils together cost Rs400. Find the cost of pen and that of a pencil
(A) 6.50, 1.50
(B) 2.50, 1.00
(C) 4.50, 1.50
(D) 6.50, 2.50

17.Solve the following system of linear equation
2(ax - by) + (a + 4b) = 0
2(bx + ay) + (b - 4a) = 0
(A) x = 1, y = 2
(B) x = -1/2, y = 2
(C) x = 1/2 , y = -2
(D) None of these

18.If a₁/a₂ ≠ b₁/b₂ then a₁x + b₁y + c₁ = 0 & a₂x + b₂y + c₂ = 0 will represent ______line

19.The solution of the system of equations 2x -3y+4xy = 0 and 6x + 5y - 2xy = 0 is
(A) x = 0, y = 0
(B) x = 1, y = -2
(C) Both 'a' and 'b'
(D) None of these.

20.Which of the following system of equations is consistent?
(A) 3x - y = 1, 6x - 2y = 5
(B) 4x + 6y - 7 = 0, 12x + 18y - 21 = 0
(C) 4x + 7y = 3, 8x + 14 y = 7
(D) 6x + 2y = 3, 5x + 6y = - 2.

21.The coordinates of the point where the line 2(x - 3) = y - 8 meet the x-axis is
(A) (3, 0)
(B) (2, 0)
(C) (-1, 0)
(D) (0, -1)

22.The coordinates of the points where the lines 3x - y = 5, 6x - y = 10 meet the y-axis are
(A) (0, -5), (0, -10)
(B) (-5, 0), (10, 0)
(C) (5, 0), (0, -10)
(D) (0, -5), (0, -10)

23.Which of the following system of equations has infinitely many solutions?
(A) 5x - 4y = 20,  7.5x - 6y = 0
(B) 2x -3y = 5,  3x - 4.5y = 7.5
(C) x + 5y - 3 = 0,  3x + 15y - 9 = 0
(D) All of these.

24.A system of simultaneous linear equation is said to be consistent, if it has __________ solution.

25.If x/b = y/a, bx + ay = a² + b², then the values of (x, y) are
(A) (a, b)
(B) (-a, -b)
(C) (b, -a)
(D) (b, a).

26.A system of simultaneous linear equation is said to be ________ if it has no solution.

27.The coordinates of the points where the lines 5x - y = 7, 10x + y = 15 meet the y-axis
(A) (0, -7), (0, 15)
(B) (-7, 0), (15, 0)
(C) (7, 0), (0, -15)
(D) (0, -7), (0, -15)

28.If a₁x + b₁y + c₁ = 0 & a₂x +b₂y + c₂ = 0 then what will be the condition of consistency of infinite many solution ?

29.If a₁/a₂ = b₁/b₂ ≠ c₁/c₂ then what will be the condition of a₁x + b₁y + c₁ = 0 & a₂x +b₂y + c₂ = 0?

30.Sum of two numbers in 48 and their difference is 20. Find the numbers.

31.If the difference of two numbers is 26 and one number is three times the other, find the numbers

32.The sum of two numbers is 128 and their difference is 16. Find the number
(A) 70 , 52
(B) 72, 56
(C) 70 , 56
(D) 72 , 52

33.The solution of the system of equations 2x + 3y + 5 = 0 and 3x - 2y - 12 = 0 is _________
(A) x = - 3, y = - 2
(B) x = 2, y = - 3
(C) x = 3, y = - 2
(D) x = 12, y = 13

34.The solution of the system of equations 2x + 5y / xy = 6 and 4x - 5y / xy + 3 = 0 (where x ≠ 0, y ≠ 0) is
(A) x = 1, y = 2
(B) x = 0, y = 0
(C) x = - 1, y = 2
(D) x = 1, y = -2

35.Solve for x and y :
47x + 31y = 63
31x + 47y = 15
(A) x = -2, y = 1
(B) x = 2, y = -1
(C) x = 2, y = 1
(D) None of these

36.Solve (2u + v) = 7uv
3(u + 3v) = 11uv
(A) u = 0, v = 0
(B) u = 1, v = 3/2
(C) Both of these
(D) None of these

37.Solve:
x + 2y + z = 7
x + 3z = 11
2x - 3y = 1
(A) x = 1, y = 2, z = -1
(B) x = 2, y = 1,z = 3
(C) x = -1, y = -2, z = 1
(D) x = 3, y = 1, z= - 2

38.Solve x + y + 2z = 9
2x - y + 2z = 6
3x + y + 4z = 17
(A) x = 0,y = 1,z = 2
(B) x = -1,y = -2,z = -3
(C) x =1,y= 2, z = 3
(D) None of these

39.For what value of k, will the following system of equations x + 2y + 7 = 0, 2x + ky + 14 = 0 represent coincident lines
(A) 2
(B) 3
(C) 4
(D) 5

40.Solve: 4x + 6/y = 15
6x - 8/y = 14 and hence, find 'p' if y = px - 2.
(A) 3/4
(B) 1
(C) 0
(D) 4/3

41.Show that the following system of equations has unique.solution
2x - 3y = 6
x + y = 1
(A) Unique solution
(B) No solution
(C) Infinite
(D) None of these

42.For what value of k the following system of equations has a unique solution:
x - ky = 2
3x + 2y = -5
(A) k ≠ -2/5
(B) k ≠ -1/3
(C) k ≠ -2/3
(D) None of these

43.Solve 2x + 3y = 11 and 2x - 4y = -24 and hence find the value of 'm' for which y = mx + 3
(A) 1
(B) 2
(C) -2
(D) -1

44.The coordinates of the point where the line 5(x - 4) = 2y - 25 meet the x-axis
(A) (4, 0)
(B) (5, 0)
(C) (-1, 0)
(D) (0, -1)

45.The taxi charges in a city comprise of a fixed charge together with the charge for the distance covered. For a journey of 10 km the charge paid is Rs75 and for a journey of 15 km the charge paid is Rs110.What will a person have to pay for traveling a distance of 25 km.
(A) 220
(B) 240
(C) 200
(D) 180

46.Solve the following system by the method of elimination( substitution)
2x - y = 5
3x + 2y = 5
(A) x = 2, y = 1
(B) x = 1, y = 1
(C) x = 3, y = 1
(D) None of these

47.What number must be added to each of the number 5,9,17,27 to make the numbers in proportion?
(A) 4
(B) 5
(C) 6
(D) 3

48.The difference between two numbers is 26 and one number isthree times the other. Find them.
(A) 30, 13
(B) 35, 12
(C) 39, 31
(D) 39, 13

49.Find the value of k for which the following syatem of equation has no solutions:
2x + ky = 1; 3x - 5y = 7
(A) 0
(B) 10/3
(C) -(10/3)
(D) 1

50.For what value of k the following equations are inconsistent?
x - 4y = 6, 3x + ky = 5
(A)10
(B)12
(C)-12
(D)-10

51.The ratio of two persons is 9:7 and the ratio of their expenditure is 4:3. If each of them saves Rs 200 per month, find their monthly incomes
A) 1000,800
(B) 1800,1400
(C) 1600,1200
(D) 1600,1400

52.Solve the following system of equation by the method of cross-multiplication. 11x + 15y = -23
7x - 2y = 20
(A) x = 2, y = 2
(B) x = 3, y = -3
(C) x = 2, y = -3
(D) None of these

53.Solve the following system of linear equation by using the method of elimination by equating the coefficients.
√3x - √2y = √3
√5x + √3y = √2
(A) x = 5(√10 - 3), y = 5√15 - 8√6
(B) x = 5, y = 5
(C) x = 5(√10+3), y = 5 (√15 + 8 √6)
(D) The given equations are
√3x - √2y = √3
√5x + √3y = √2

54.For what value of p does the system of equations 4x - py = 0, 5x + 6y = 0 has nonzero solution?
(A) p = - 8
(B) p = -24/5
(C) p = -5/6
(D) p = -(3/8)

<3M>

55. (a) Solve:
217x + 131y = 913 =..(i)
131x + 217y = 827 ..(ii)
(b) For what value of the system of Equation
3x + 5y =0 
ux + 10y = 0 has unique solution

<6M>

56.The sum of a two - digit number and the number obtained by reversing the digits is 66. If the digits of the number differ by 2, find the number. How many such numbers are there?

57.Solve:
ax + by = a - b
bx - ay = a + b
By cross multiplication method.

58.A man has only 20 paise and 25 paise coins in his purse. If he has 50 coins in all totaling Rs 11.25 How many coins of each does he have?

59.On selling a tea set at 5% loss and a lemon set at 15% gain, a crockery seller gained Rs. 7.0 If he sells the tea set at 5% gain and the lemon set at 10% gain, the gain isRs 13. Find the actual price of the tea set and the lemon set.

60.A boat goes 30km upstream and 44km downstream is 10hrs. In 13 hrs it go 40km upstream and 55 km downstream. Determine the speed of the stream and that of boat in still water.

61. (a) Use elimination method to find all possible solutions of the following pair of equations.
2x + 3y = 8
4x + 6y = 7
(b) Determine the value on of ' u ' so that the following equations have no solutions.
(3u+1) x+3y - 2 = 0
(u²+1) x+(u-2)y - 5 = 0

62.a) The taxi charges in a city comprise of a fixed charge together with the charge for the distance covered. For a journey for 10km the charge paid is Rs 75 and for a journey of 15km the charge paid Rs 110. What will a person have to pay for traveling a distance of 25km.
(b) In ΔABC, ∠C = 3∠B = 2(∠A+∠B) Find the three angles.

63.Solve the given Equation by using the method of substitution.
2x+3y = 9
3x+4y = 5

64. Solve:
1/2x - 1/y = - 1
1/x + 1/2y = 8

65. Solve by cross multiplication, the following system of Equation:
x+y = 7
5x+12y = 7

66. Solve the following system of Equation -
8x - 3y = 5xy
6x - 5y = 2xy

67.a) For what value of 'u' will the following pair of Equation have infinitely many solutions.
ux+3y-(u-3) = 0
12x+uy - u = 0
(b) For what value of p does the pair of Equations given below has uniquesolution?
4x+py+8 = 0
2x+2y+2 = 0

68.A man sold a chair and a table together for Rs 1520 .There is a profit of 25% on the chair and 10% on table. By selling them together for Rs 1535, he could have made a profit of 10% on the chair and 25% on the table. Find the cost price of each.

69.Solve the given Equation by using the method of elimination by the coefficients:
x/10 + y/5 + 1 = 15
x/8 + y/6 = 15