#Class 9 #MCQ #Chapter_4 #linear_equations_in_two_variables

Maths Learning Centre, Jalandhar
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https://www.youtube.com/@MathematicsOnlineLectures Class IX: Linear Equations in Two Variables Mathematics
MULTIPLE CHOICE QUESTIONS
1. The equation 2 5 7
x y
  has a unique solution, if x, y are:
(A)natural numbers (B) positive real numbers
(C) real numbers (D) rational numbers
2. The graph of the linear equation 2 3 6
x y
  cuts the y-axis at the point
(A)(2, 0) (B) (0, 3) (C) (3, 0) (D) (0, 2)
3. Any point on the x-axis is of the form
(A)(x, y) (B) (0, y) (C) (x, 0) (D) (x, x)
4. Any point on the line y = x is of the form
(A)(a, a) (B) (0, a) (C) (–0, a) (D) (a, –a)
5. The graph of y = 6 is a line.
(A)parallel to x-axis at a distance 6 units from the origin
(B) parallel to y-axis at a distance 6 units from the origin
(C) making an intercept 6 on the x-axis
(D)making an intercept 6 on both the axis.
6. The graph of the linear equation 2x + 3y = 6 is a line which meets the x-axis at the point:
(A)(0, 2) (B) (2, 0) (C) (3, 0) (D) (0, 3)
7. The graph of the linear equation y = x passes through the point:
(A)
3 3
,
2 2

 
 
 
(B)
3
0,
2
 
 
 
(C) (1, 1) (D)
1 1
,
2 2

 
 
 
8. How many linear equation in x and y can satisfy x = 1 and y = 2?
(A)only one (B) two (C) infinitely many (D) three
9. The point of the form (a, a) always lies on:
(A)x-axis (B) y-axis (C) on the line y = x (D) on the line x + y = 0
10. The point of the form (a, –a) always lies on the line
(A)x = a (C) y = a (C) y = x (D) x + y = 0 .
11. Solve : 37x + 41y = 70
41x + 37y = 86
(A) x = 3 and y = – 1 (B) x = 3 and y = 5 (C) x = 4 and y = 7 (D) x = 9 and y = 5
12. 37 pens and 53 pencils together cost `320, while 53 pens and 37 pencils together cost `400. Find the
cost of a pen.
(A) `6.50 (B) `2.50 (C) `3.50 (D) `5.50
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13. In 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.
(A) 93 (B) 21 (C) 54 (D) 79
14. The sum of a two digit number and the number formed by interchanging its 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.
(A) 64 (B) 33 (C) 24 (D) 12
15. 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.
(A)
12
25
(B)
11
13
(C)
11
17
(D)
11
19
16. 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.
Determine the fraction.
(A)
7
18
(B) 5/13 (C) 9/2 (D) 1/5
17. If
2x 1 3y 1
2
3 2
 
  &
3x 1 2y 1
2
2 3
 
  , then
(A) x = 1, y = 2 (B) x = 1, y = 1 (C) x = 1, y = 1/2 (D) x = 1/2, y = 1/2
18. If 3ax + 2by = 5ab and 5ax – 3by = 2ab, then
(A) x = b, y = a (B) x = a, y = b (C) x = y = a (D) x = y = b
19. If
a b
0
x y
  and
2 2
2 2
ab a b
a b
x y
   , then
(A) x = y = b (B) x = y = a (C) x = a, y = b (D) x = b, y = a
20. If
x y
a b
 and 2 2
ax by a b
   , then
(A) x = a, y = b (B) x = b, y = a (C) x = a/2, y = b/2 (D) x = b/2, y = a/2
21. An inconsistent system of two linear equations in two variables will have
(A) one solution (B) two solutions
(C) no solution (D) more than two solutions.
22.
x y 0
2x 2y 0
 


 

has
(A) no solution (B) one solution
(C) two solutions (D) more than two solutions.

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23. The graphs of 2x + 3y – 6 = 0, y = 2/3, x = 2 and 4x – 3y = 6 intersect in
(A) four points (B) one point
(C) in no point (D) in infinite number of points.
24. Yamini and Fatima, two students of class IX of a school, together contributed Rs. 100 towards the
Prime Minister’s Relief Fund to help the earthquake victims. A linear equation which satisfies this
data is
(A) x – y = 100 (B) x + y = 100 (C) x + 2y = 100 (D) 2x + y = 100.
25. The value of k for which the system of equations
kx – y = 2, 6x – 2y = 3
has a unique solution, is
(A) = 3 (B)  3 (C) 0 (D) = 0.
26. The value of k for which the system of equations 2x + 3y = 5, 4x + ky = 10
has infinite number of solutions, is
(A) 1 (B) 3 (C) 6 (D) 1.
27. The value of k for which the system of equations x + 2y – 3 = 0 and 5x + ky + 7 = 0 has no
solution, is
(A) 10 (B) 6 (C) 3 (D) 1.
28. If am  bl, then the system of equations ax + by = c, lx + my = n
(A) has a unique solution (B) has no solution
(C) has infinitely many solutions (D) may or may not have a solution.
29. The present ages of a brother and sister in the ratio of 2 : 3. Ten years hence, the ratio will be 3 : 4,
find their present ages.
(A) brother’s age = 30 years (B) sister’s age = 20 years
(C) brother’s age = 20 years (D) sister’s age = 30 years .
30. Solving 4x + 3y = 25 and 5x – 2y = 14 results in –
(A) x = 4 (B) x = 3 (C) y = 3 (D) y = 4.
31. If the point (3, 4) lies on the graph of the equation 3y = ax + 7, the value of a is
(A)
5
3
(B) 1.6 (C) 1 (D)
2
5
.
MATRIX MATCHING
32. Column–II give solution for equation in column–I match them correctly
Column–I Column–II
(A)2x + y = 7 (p) (0, 9)
(B) x – 2y = 4 (q) (1, 5)
(C) x – 4y = 0 (r) (0, 0)
(D)px + y = 9 (s) (4, 0)

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33. Match them correctly
Column–I Column–II
(A)x = a (p) x-axis
(B) y = a (q) st. line parallel to x-axis
(C) y = mx (r) st. line parallel to y-axis
(D)y = 0 (s) st. line passing through origin.
INTEGER TYPE QUESTIONS
34. In a picnic there are boys and girls. Fifteen girls leave, then the boys and girls are left in the ratio of
2: 1. Later 45 boys leave and the ratio changes to 1 : 5. The number of girls in the beginning was 8
 then find .
35. A man can do a piece of work in 30 hours. He and his son together finish it in 20 hours. The son
along will finish it in (8 + 4) hours, then find .
36. Find the value of k, if x = 2, y = 1 is a solution of the equation 2x + 3y = k.
37. In some countries, temperature is measured in Fahrenheit, whereas in countries like India, it is
measured in Celsius. Here is a linear equation that converts Fahrenheit to Celsius
9
F C 32
5
  , if
the temperature is 40º C, the temperature in Fahrenheit is 13, then find 

#Class 9 #MCQ #Chapter_4 #linear_equations_in_two_variables

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#Class 9 #MCQ #Chapter_4 #linear_equations_in_two_variables