Class 9 Mathematics MCQ Linear Equations In Two Variables

Question :All linear equations in two variables have ————– .
(a) One solution
(b) Infinitely many solutions
(c) Three solutions
(d) Two solution

Question :The equation of a line parallel to x-axis and 3 units above the origin is
(a) x = -3
(b) x = 3
(c) y = -3
(d) y = 3

Question :If (2, 0) is a solution of the linear equation 2x +3y = k, then the value of k is:
(a) 4
(b) 6
(c) 5
(d) 2

Question :The graph of x = 3 is a line:
(a) Parallel to x-axis at a distance of 3 units from the origin
(b) Parallel to y-axis at a distance of 3 units from the origin
(c) Makes an intercept 3 on x-axis
(d) Makes an intercept 3 on y-axis

Question : The value of k if x = 2, y = 1 is a solution of equation 2x – k = – 3y is:
(a) 6
(b) 5
(c) 7
(d) -7

Question : For two lines 2x + y = 1 and x – y = 2 if the x coordinate of the common point is 1 what is the y coordinate?
(a) -1
(b) 2
(c) -2
(d) 3

Question : The sum of two numbers is 8 and the sum of their reciprocals is 8/15. Find the numbers.
(a) 5, 3
(b) 7, 1
(c) 4, 4
(d) 2, 6

Question : Solve for x and y in the following question.

(A) x = 1, y = 2
(b) x = 2, y = 1
(c) x = 2 y = 1/2
(d) x = 1/2 y = 2

Question : Match the following.System of equations           Solutions
(P) 2x – 3y + 15 = 0             (i) x = 3, y = 5
3x – 5 = 0
(Q) 2x – y = 1                      (ii) x = 1, y = 4
4x + 3y = 27
(R) x + 2y – 3 = 0                (iii) x = 5/3 y = 55/9
3x – 2y + 7 = 0
(S) 4x + y/3 = 16/3              (iv) x =– 1,y = 2
x/2 + 2y/4 = 5/2
(a) (P) → (iii); (Q) → (iv); (R) → (i); (S) → (ii)
(b) (P) → (iii); (Q) → (i); (R) → (iv); (S) → (ii)
(c) (P) → (iii); (Q) → (ii); (R) → (iv); (S) → (i)
(d) (P) → (ii); (Q) → (i); (R) → (iv); (S) → (iii)

Question :Which of the following graphs represent the lines 2x + 4y = 8 and 3x – 4y = 12 ?

Question :Fill in the blanks.
(i) If pair of linear equations is consistent, then it has either P or Q solution(s).
(b) If the pair of linear equation is inconsistent, then it has R solution(s).
(c) If the graph of two linear equations coincide, then they have S solution(s).
        P             Q              R            S
(a) no          infinite      unique      infinite
(b) unique    infinite          no        infinite
(c) no          infinite      unique      unique
(d) unique    no            infinite      no

Question : Read the statements carefully and state ‘T’ for true and ‘F’ for false.
(i) The pair of linear equations x + 2y = 5 and 7x + 3y = 13 has unique solution x = 2, y = 1.
(b) √2x + √3y = 0, √3x − √8y = 0 has no solution.
(c) The values of p and q for which the following system of equations 2x – y = 5, (p + q)x + (2p – q)y = 15 has infinite number of solutions, is p = 1 and q = 5.
        (i)    (ii)   (iii)
(a)    T      F     T
(b)    T     T      F
(c)    F     T      T
(d)    F     F      T

Question : The sum of the digits of a two-digit number is 12. The number obtained by interchanging the two digits exceeds the given number by 18. Find the number.
(a) 57
(b) 75
(c) 85
(d) 58

Question : The denominator of a rational number is greater than its numerator by 3. If 3 is subtracted from the numerator and 2 is added to the denominator, the new number becomes 1/5 . Then the original number was _______.
(a) 7/11
(b) 3/5
(c) 5/8
(d) 4/7

Question : If am = bl and bn ≠ cm, 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.

Question : The value of k, for which the system of equations kx – 3y + 6 = 0, 4x – 6y + 15 = 0 represent parallel lines, is _______.
(a) 1
(b) 2
(c) 3
(d) 4

Question : If the system of equations
    2x + 3y = 7
    2ax + (a + b)y = 28
has infinitely many solutions, then the values of a and b respectively are _______.
(a) 2, 5
(b) 5, 8
(c) 4, 8
(d) 3, 6

Question : In a ΔABC, ∠C = 3∠B = 2(∠A + ∠B). The three angles will be _______.
(a) 20°, 40°, 120°
(b) 30°, 60°, 90°
(c) 45°, 45°, 90°
(d) 90°, 40°, 50°

Question : ax + by + c = 0 does not represent an equation of line when _______.
(a) a = c = 0, b ≠ 0
(b) b = c = 0, a ≠ 0
(c) a = b = 0
(d) a = b ≠ 0

Question : The ratio of a 2-digit number to 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 tens place, what is the number ?
(a) 63
(b) 36
(c) 24
(d) 40

Question : How many values of c, for which the systemof equations 6x + 3y = c – 3, 12x + cy = c has infinitely many solutions?
(a) 1
(b) 2
(c) 3
(d) Infinite

Question : Sum of two numbers is 64 and their difference is 22. Find the numbers.
(a) 42, 22
(b) 43, 21
(c) 40, 24
(d) 50, 28

Question : If a pair of linear equations in two variablesis consistent, then the lines represented by two equations are
(a) Always intersecting
(b) Parallel
(c) Always coincident
(d) Intersecting or coincident

Question : The solution of the system of equations 2x 5y/xy = and 4x – 5y/xy+ 3=0 (where x ≠ 0, y ≠ 0), is _______.
(a) 1, 2
(b) 0, 0
(c) –1, 2
(d) 1, –2

Question : Value of x in pair of linear equations 36x + 24y = 702 and 24x + 36y = 558 is
(A) 33/2
(b) 145/7
(c) 16
(d) 17

Question : Which of the following linear equation coincide with the line 4x + 5y = 15?
(a) 8x + 10y = 25
(b) 2x + 3y = 7
(c) 7x + 14y = 17
(d) 12x + 15y = 45

Question : Arun and Prabhat have some books with them. Once Prabhat said to Arun that, if Arun gives 3 books to Prabhat then Arun will have only 1/2 of the books that Prabhat will have with him. Then Arun asked frankly that if Prabhat gives him only two books (to Arun), then Prabhat will have as many books as Arun will have. The total number of books that Arun and Prabhat have with them is _______.
(a) 25
(b) 56
(c) 30
(d) Can’t be determined

Question : Places M and N are 90 km apart from each other on a national highway. A truck starts from M and another from N at the same time. If they go in the same direction, then they meet in 9 hours and if they go in opposite directions they meet in 9/7 hours. The speed of the trucks are _______.
(a) 90 km/hr, 40 km/hr
(b) 40 km/hr, 30 km/hr
(c) 20 km/hr, 60 km/hr
(d) 50 km/hr, 12 km/hr

Question : A boat goes 32 km upstream and 36 km downstream in 7 hours. In 9 hours, it can go 40 km upstream and 48 km downstream. If x represents the speed of the boat in still water in km/hr and y represents the speed of the stream in km/hr, then_______.
(a) x + y = 12, x – y = 8
(b) x + y = 5, x – y = 11
(c) x + y = 6, x – y = 10
(d) x + y = 10, x – y = 6

Question : At the end of the year 2002, Ram was half as old as his grandpa. The sum of the years in which they were born is 3854. Age of Ram at the end of year 2003 is _______.
(a) 50 years
(b) 35 years
(c) 51 years
(d) 36 years

Question : On selling a tea-set at 5% loss and lemonset at 15% gain, a crockery seller gains ₹ 7. If he sells the tea-set at 5% gain and the lemon-set at 10% gain, he gains ` 13. Find the actual prices of the tea-set and the lemon-set.
(a) ₹ 100, ₹ 80
(b) ₹ 90,   ₹ 100
(c) ₹ 120, ₹ 60
(d) ₹ 150, ₹ 80