Download pair of linear equations

Chapter-wise questions
Pair of linear equations
1. For what value of p the following pair of linear equations has infinitely
many solutions.
x + y – k = 0 and x + y + (k–12) = 0
6
3
18
9
2. Find the value of a and b so that the equations has infinitely many
solutions.
3x + 8y – 7 = 0 and (a+b)x + (a+4b) = 6a – b+2
3. Find the number of solutions of the following pair of linear equations.
2x + 3y = 5 and 3x + 2y – 6 = 0
4. Solve the following system of linear equations graphically and shade the
region between the two lines and X axis. 5x + 3y = 15 and 7x + 4y = 28
5. A man sold a chair and table together for Rs 1520 thereby making a profit of 25%
on the chair and 10% on the table. By selling them together for Rs 1535 he would
have made a profit of 10% on the chair and 25% on the table. Find the cost price of
each.
6. Draw the graph of 2x+y+6 and 2x–y+2 = 0. Shade the region bounded by
these lines and the X-axis. Find the area of the shaded region.
7. Solve the following system of linear equations graphically: x – y = 1, 2x+y
= 8. Shade the are bounded by these two lines and y-axis.
8. Solve the following system of linear equations graphically: 2x+y–5 = 0,
x+y–3 = 0. Find the points where the lines meet the y-axis.
9. Solve the following system of linear equations graphically: 3x–5y = 19; 3y–
7x+1 = 0, Does the point (4,9) lie on any of these lines? Write its equation.
[(x = -2, y = -5); yes on 3y–7x+1 = 0]
Chapter-wise questions
10. Solve the following system of linear equations.
i) (a–b)x + (a+b)y = a² – 2ab – b²
(a+b)(x+y) = a² + b²
ii) 4 +5y = 7, 3 = 4y = 5
iii) 44 + 30 = 10; 55 + 40 = 13
(x+y) (x–y)
(x+y) (x–y)
iv) ax + by = a – b; bx – ay = a+b
v) x + y = a – b; ax – by = a²+b²
vi) 11 – 7 = 1; 9 – 4 = 6
v u
v u
vii) x – y = a+b; x – y = 2
a b
a² b²
x
x
11. The sum of the numerator and the denominator of a fractions is 8. If 3 is
added to both the numerator and the denominator, the fractions becomes
3 . Find the fraction.
4
12. Father’s age is three times the sum of ages of his two children. After 5 years
his age will be twice the sum of age of his two children. Find the age of
father.
13. Two places A and B are 120 km, apart from each other on a highway. A car
starts from A and another from B at the same time. If they move in the same
direction, they meet in 6 hours and if they move in opposite directions, they
meet in 1 hour and 12 minutes. Find the speeds of the cars.
14. The sum of a two digit number and the number obtained by reversing the
order of its digits is 99. If the digits differ by 3, find the number.
15. A man travels 370km partly by train and partly by car. If he covers 250 km
by train and the rest by car, it takes him 4 hours. But if he travels 130 km
by train and the rest by car, he takes 18 minutes longer. Find the speed of
the train and that of the car.
Chapter-wise questions
16. A boat goes 16 km upstream and 24 km downstream in 6 hours. It can go
12km upstream and 36 km downstream in the same time. Find the speed
of the boat in still water and the speed of the stream.
17. 5 books and 7 pens together cost Rs 79 whereas 7 books and 5 pens
together cost Rs 77. Find the total cost of 1 book and 2 pens.
18. Find the value of k so that the following pair of linear equation has infinitely many
x + 3y = 7
solutions.
7x + 21y = (k – 3)
19. For what values of a and b will the equations 2x+3y = 7, (a–b)x + (a+b)y = 14
represent coincident lines.
20. Check whether the following pair of equations represent parallel lines,
2x+4y=7, 3x+6y = 21
21. For what value of k, the following equations are inconsistent?
x–4ky = 6, 3x+5y = 5
22. For what value of k, the following equations 3x–y–5 = 0 and 6x–2y–k = 0 has no
solution.
23. Solve the following system of linear equations
6(ax+by) = 3a + 2b
6(bx – ay) = 3b – 2a.
24. Solve for x and y: x +
6
8
= 6, 3x –
=5
y
y
25. Solve for x and y : 4x +
y
3
=
8
x + 3y =
,
3 2
4
26. Solve :
2(ax–by) + (a+4b) = 0
2 (bx+ay) + (b–4a) = 0
5
2
Chapter-wise questions
27. Represent the following pair of equations graphically and write the coordinate of
points where the lines intersect X-axis.
x + 3y = 6
2x – 3y = 12
28. Solve for x and y: 8x – 9y = 6xy, 10x + 6y = 19xy
29. The sum of digits of 2 digit number is 15. The number obtained by interchanging
the digits exceeds the given number by 9. Find the number.
y–1
x–1 y+1
= 8 and
+
= 9
3
2
2
3
31. Solve the following system of linear equations graphically.
30. Solve for x and y :
x+1
+
5x – 6y + 30 = 0
5x + 4y – 20 = 0
Also find the vertices of the triangle formed by the above two lines and X-axis.
32. Solve the following system of linear equations graphically.
2x + 3y = 12
2y – 1 = x 33. Draw the graph of the equations
4x – y – 8 = 0 and 2x – 3y + 6 = 0
Also determine the vertices of the triangle formed by the lines and the X-axis
34. A train crosses 210m and 122m long tunnels in 25 and 17 seconds respectively.
Find the length of the train and also find speed of the train.
35. The taxi charges in a city comprise of a fixed charge together with the charge for
the distance covered. For a journey of 10km the charge paid Rs. 75 and for a
journey of 15 km the charge paid Rs. 110. What will a person pay for travelling a
distance of 25 km?
36. The difference of two numbers is 4. If the difference of their reciprocals is
the two numbers.
4
, find
21
Chapter-wise questions
37. The sum of the squares of two consecutive odd numbers is 650. Find the
integers.
38. 2 women and 4 men can finish a work in 4 days while 2 women and 1 man can
finish the same work in 10 days. In how many days 1 man alone and 1 woman
alone can finish the work.
39. A man travels 600 km partly by train and partly by car. If he covers 400 km by train
and the rest by car, it takes him 6hr 30 minutes. But if travels 200. km by train and
the rest by car, he takes half an hour longer. Find the speed of the train and that of
car.