CBSE Class 10 Maths HOTs Pair Of Linear Equations In Two Variables Set 05

Say True (T) or False (F).

Question. System of equations: \( x + y = 2xy \) and \( 2x + 3y = 5xy \) has two sets of solutions.
Answer: T (0, 0) & (1, 1)

Question. Lines represented by equations \( x = 2 \) and \( y = -7 \) has one solution in common.
Answer: T

Question. Line given by equation \( 3x - 7y = 0 \) will not passes through origin.
Answer: F

Question. Lines given by \( x + 2y = 3, 3x - y = 2 \) and \( 7x + y = 8 \) are concurrent at point (1, 1).
Answer: T

Question. We can not solve the system of equations \( x + y = 3 \) and \( \frac{1}{x} + \frac{1}{y} = \frac{5}{6} \) graphically.
Answer: T

Question. Image of the point (2, 3) under x axis is (- 2, 3).
Answer: F

Question. Image of the point (- 7, - 5) under y axis is (7, - 5).
Answer: T

Question. Equations \( x + y = 0 \) and \( 2x + 2y = 0 \) have infinitely many solutions in common.
Answer: T

Question. We can find the image of origin.
Answer: F

Question. We can solve a system of linear equations in two variables if system satisfy the condition of infinitely many solutions.
Answer: F

Fill in the Blank.

Question. Line represented by equation \( 2x + 3y = 8 \) intersects x-axis at ________.
Answer: (4, 0)

Question. Each linear equation in two variables has ________ set of solutions.
Answer: Infinite

Question. For value 'k' = 3 system: \( x + ky = 2 \) and \( 4x + 12y = 8 \) has ________ solutions.
Answer: Infinite

Question. System: \( ax + by = 3 \) and \( 3ax + 3by = 4 \) always has ________ solution for any non zero real value of \( a \) and \( b \).
Answer: No

Question. Set of common solution for system \( 2x + 11y = 0 \) and \( 8x + 5y = 0 \) is ________.
Answer: \( x = 0 \text{ & } y = 0 \)

Question. Linear equation of the form \( ax + by = c \) where \( a \neq 0, b \neq 0, c \neq 0 \) can not be parallel to ________ and ________.
Answer: x-axis and y-axis

Question. Nature of triangle formed between coordinate axis and line represented by equation \( x + y = 4 \) is ________.
Answer: right angled Isosceles

Question. Lines given by \( x + y = 3 \) and \( -x + y = 3 \) meet y axis at point ________.
Answer: (0, 3)

Question. System of equations \( x + 2y = 3 \) and \( x + 3y = 3 \) is ________.
Answer: consistent

Question. \( x + y = 0 \) and \( x - y = 0 \) pair of linear equations has ________ solution.
Answer: unique

Question. System of equations \( 3x + 4y = 8 \) and \( kx + 8y = 16 \) is consistent for the value of \( k = \) ________.
Answer: k = 6

Question. System of equations \( x + y = 4 \) and \( 3x + ky = 8 \) is consistent for value of \( k \neq \) ________.
Answer: k ≠ 3

Question. Graph of line \( x + 4 = 0 \) is parallel to ________.
Answer: y-axis

Question. Graph of line \( y - 7 = 0 \) meet y axis at ________.
Answer: (0, 7)

Question. For a pair of linear equations in two variables of the form \( a_1x + b_1y = c_1 \) and \( a_2x + b_2y = c_2 \) may have zero solutions only if values of \( c_1 \) and \( c_2 \) are ________ and \( \frac{a_1}{a_2} \boxed{} \frac{b_1}{b_2} \).
Answer: zero and ≠

MCQs with more than one correct options.

Question. Consistent solutions means
(a) No solution
(b) Unique solution
(c) Infinitely many solutions
(d) All of the options
Answer: (b) & (c)

Question. Lines represented by equations \( x = a \) and \( y = b \) are :
(a) perpendicular to each other
(b) Intersects at a point where \( x = a \text{ & } y = b \)
(c) parallel to each other
(d) Has no solution.
Answer: (a) & (b)

Question. Value of \( k \) for which system of equations : \( kx + 2y = 3 \) and \( 2x + ky = 7 \) has a unique solution can not be equal to
(a) 2
(b) -2
(c) both (a) & (b)
(d) No such value exists.
Answer: (a), (b) & (c)

Question. A number when added to its reciprocal result becomes double of the number then number is
(a) 3
(b) 2
(c) 1
(d) -1
Answer: (c) & (d)

Question. Lines represented by equations \( x = y \) and \( x = -y \) are :
(a) passing through origin
(b) parallel to each other
(c) perpendicular to each other
(d) coincident lines
Answer: (a) & (c)

Question. Possible values of \( k \) for which system \( 2x - 7y = k \) and \( 3x + 2y = 5 \) has unique solution :
(a) 2
(b) 3
(c) 4
(d) No such value of k exist
Answer: (a), (b) & (c)

Question. A number when added to its square result is double of square of number then possible numbers are
(a) 0
(b) -1
(c) 2
(d) 1
Answer: (a) & (d)

Question. Graph of equation represented by \( x + 3 = 0 \) is
(a) Perpendicular to y-axis
(b) Perpendicular to x-axis
(c) Parallel to y-axis
(d) Parallel to x-axis.
Answer: (b) & (c)

Question. Line represented by equation \( 2x + 3y = 5 \) meet :
(a) x-axis at \( (\frac{5}{2}, 0) \)
(b) y-axis at \( (0, \frac{5}{2}) \)
(c) Line : \( x + y = 2 \) at (1, 1)
(d) Line : \( x + y = 0 \) at origin
Answer: (a), (b) & (c)

Question. Which of the following system has unique solution :
(a) \( x + y = 2 \text{ & } x - y = 0 \)
(b) \( (x + 1)^2 + (y - 2)^2 = x^2 + y^2 \text{ & } x + y = 7 \)
(c) \( 3ax + 2by = 8c \) and \( 6ax + 4by = 4c \)
(d) \( x + y = 0 \text{ & } 3x - 2y = 0 \)
Answer: (a) & (d)