Download Delhi Public School , Allahabad

Delhi Public School , Allahabad
Chapter – Linear Equations
Class – X (Mathematics)
1. Find the value of k for which the equation
kx – 5y = 2 and 6x + 2y = 7 have no solution.
2. Find the value of k for which the given pairs
of linear equations have a unique solution.
2x + 3y – 5 = 0 and kx – 6y – 8 = 0
3. Find the value of k for which the given pairs
of linear equations have a unique solution.
3kx + 6y = √ and √ x + √ y =√
4. If 2x + y = 10 and 3x + 6y = 12 represent
parallel lines, then determine the value of .
5. If the graphical representation of the
equations
3x + y = 6 and 6x + 8y = 12 are coincident
lines, find the value of .
6. Find the value of m for which the pair of
linear
equations
2x+3y–7=0
and
(m – 1 )x + (m+1)y = 3m – 1 has infinitely
many solutions. [CBSE 10]
7. Find the number of solutions of the following
pair of linear equations.
x + 2y – 8 = 0 and 2x + 4y = 16 [CBSE 09]
8. Find the value of k for which the system of
equations 3x + 5y = 0 , kx + 10y = 0 has a nonzero solutions.
9. Is x = - 2 a solution of the equation
x2 – 2x + 8 = 0
[CBSE 08]
10. Is x = - 4 a solution of the equation
2x2 + 5x – 12 = 0
[CBSE 08]
11. Find the value of K for which each of the
following systems of equations has no
solutions.
(a) kx + 3y = 3, 12x + ky = 6 [CBSE 98,99]
(b) 3x + y = 1, (2k – 1 )x + ( k – 1 )y = (2k + 1)
[CBSE 2000]
12. Find the value of K for which each of the
following system of linear equations has an
infinite number of solutions.
(a) 2x + 3y = 7,
(k – 1 )x + (k+2)y = 3k [CBSE 01]
(b) (k – 1 )x – y = 5,
(k+1)x + (1 – k )y = (3k + 1)
[CBSE 03]
13. Find the value of a and b for which the
following system of linear equations has
infinite number of solutions.
2x – 3y = 7, (a+b)x – (a+b – 3 )y = 4a + b
[CBSE 02]
14. Show that the system of equations
2x + 5y = 17, 5x + 3y = 14 has a unique
solution.
15. Show that the system of equations
3x – 5y = 11, 6x – 10y = 7 is inconsistent.
16. Show that the system of equations
4x + 6y = 7, 12x + 18y = 21 has infinitely
many solutions.
17. Solve for x and y:
[CBSE 2000,05, 09]
18. Solve for x and y:
[CBSE 2000,04 ,05]
ax + by – a + b = 0, bx – ay – a – b = 0
19. Solve for x and y:
(a – b )x + (a + b)y = a2 – 2ab – b2
[CBSE 04,08]
(a + b)x + (a + b)y = a2 + b2
20. Solve for x and y :
47x + 31y = 63, 31x + 47y = 15 [CBSE 06]
21. Solve for x and y :
6x + 3y = 7xy, 3x + 9y = 11xy (x ≠ 0, y ≠ 0)
22. Solve for x and y :
[CBSE 02C]
23. Solve for x and y :
23x + 37y = 32
37x + 23y = 88
24. Solve for x and y :
.8x + .3y = 3.8, .4x - .5y = .6
25. Solve the following pair of linear equations
for x and y:
[CBSE 06, 10]
x + y = 2ab
26. Solve for x and y :
(a) 8x – 9y = 6xy
10x + 6y = 19xy
[CBSE 07]
(b) 4x +
27. Solve for x and y :
37x + 43y = 123
43x + 37y = 117
1
[CBSE 08]
28. The sum of the numerator and the
denominator of a fraction is 4 more than
twice the numerator. If 3 is added to each of
the numerator and denominator, their ratio
becomes
2:3.
Find
the
fraction.
[CBSE 10]
29. The sum of two numbers is 8. Determine the
numbers if the sum of their reciprocals is
43. Solve the following system of linear equations
graphically
x – y = 1 , 2x + y = 8
shade the area bounded by these two lines
and the y-axis.
[CBSE 01]
44. Draw the graph of the following pair of linear
equations:
2x – y + 8 = 0 , 8x + 3y = 24
Hence find the area of the region bounded by
x = 0, y = 0 and 8x + 3y = 24.
45. Write the equation of the x-axis and y-axis.
.
[CBSE 09]
30. The sum of two numbers is 16 and the sum of
their reciprocals is
. Find the numbers.
ANSWERS
[CBSE 05]
31. The sum of the digits of a two digit number is
12. The number obtained by interchanging its
digits exceeds the given number by 18.
Find the number.
[CBSE 06]
32. The sum of the digits of a two digit number is
15. The number obtained by interchanging
the digits exceeds the given number by 9.
Find the number.
[CBSE 04]
33. The sum of the numerator and denominator
of a fraction is 8. If 3 is added to both
numerator and the denominator, the fraction
becomes . Find the fraction.
1. k = - 15
2. k ≠ - 4
3. k ≠ √
4.
5.
6. m = 5
7. infinite no. of solutions
8. k = 6
9. No
10. Yes
11. (a) k = - 6 (b) k = 2
12. (a) k = 7 (b) k = 3
17. x = b, y = -a
18. x = 1 , y = - 1
[CBSE 03]
34. Determine k , if the graph of 2x = y + k
intersects the y-axis at(0, - 8).
35. Determine k, if the graph of kx – y = 11 passes
through the point (3, 4).
36. If (5,k) is a solution of the equation 2x + y = 7,
find the value of k.
37. The line 3y + 3 = y + 5 is parallel to which
axis?
38. The line 4x + 10 = 3x + 30 is parallel to which
axis ?
39. Solve the following system of linear equations
graphically.
2x + 3y = 12, 2y – 1 = x
[CBSE 07]
40. Represent the following pairs of equations
graphically and write the co-ordinates of
points where the lines intersect y-axis :
x + 3y = 6, 2x – 3y = 12
[CBSE 08]
41. Draw the graphs of the following equations.
3x – 4y + 6 = 0, 3x + y – 9 = 0 [CBSE 06]
also determine the co-ordinates of the
vertices of the triangle formed by these lines
and the x- axis.
42. Draw the graph of x – y + 1 = 0 and
3x + 2y - 12 = 0. Calculate the area bounded
by these lines and x-axis.
[CBSE 02]
19. x = (a + b), y =
20.
21.
22.
23.
24.
25.
x=2 , y=-1
x = 1 , y = 3/2
x = 11 , y = 8
x = 3, y = -1
x=4, y=2
x = ab , y = ab
26. (a) (0,0) , (
27.
28.
29.
30.
31.
32.
33.
34.
35.
36.
37.
38.
39.
40.
41.
42.
43.
44.
45.
2
)
(b) (1, -4)
x = 1, y = 2
5/9
3 and 5
12 and 4
57
78
3/5
k=8
k=5
k = -3
x-Axis
y-Axis
x=3, y=2
( 0, 2), (0, - 4)
(-2 , 0) , (2 , 3) , (3 , 0)
Area = 7.5 sq. units
x = 3, y = 2
12 sq. units
Eq. of x axis: y = 0
Eq. of y axis: x = 0