x = 2 y = - 1 is a solution of the linear equation
- ✓x + 2y = 0
- Bx + 2y = 4
- C2x + y = 0
- D2x + y = 5
Answer: A.
View full solution →Question types
Linear Equations In Two Variables [NEW] question types
131 questions across 8 question groups — pick any mix to generate a Maths paper with step-by-step answer keys.
131
Questions
8
Question groups
5
Question types
01
M.C.Q
51 Q→02Assertion (A) & Reason (B) MCQ
8 Q→031 Marks Question
10 Q→042 Marks Questions
19 Q→053 Marks Question
19 Q→064 Marks Questions
15 Q→07Case study (4 Marks)
2 Q→085 Marks Questions
7 Q→Sample Questions
Linear Equations In Two Variables [NEW] questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
The work done by a body on application of a constant force is the product of the constant force and the distance travelled by the body in the direction of the force. If the constant force is 3 units, y is the work done and x is the distance travelled, then the linear equation in two variables to express the above statement is
- Ax = 3y
- By = 3x
- Cy = x + 3
- Dx = y + 3
The solution of the linear equation x + 2y = 8 which represents a point on y-axis, is
- A(0,4)
- B(8,0)
- C(4,2)
- D(2, 3)
The solution of the linear equation x + 2y = 8 which represents a point on x-axis, is
- A(4,0)
- B(0,4)
- C(8,0)
- D(4,2)
The positive solutums of the equation $a x+b y+c=0$ always lie in the
- A$l^2$ quadrant
- B$2^{\text {nt }}$ quadrant
- C$3^{\text {te }}$ quadrant
- D$4^{\text {te }}$ quadrant
Statement-1 (A): The graph of the linear equation $y=m x+c$ passes through the origin.
Statement-2 (R): The linear equation $a x+b y=0$ represents a straight line passing through the origin.
Statement-2 (R): The linear equation $a x+b y=0$ represents a straight line passing through the origin.
- AStatement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
- CStatement- 1 is true, Statement-2 is false.
- ✓Statement- 1 is false, Statement-2 is true.
Answer: D.
View full solution →Statement-1 (A): The graph of the linear equation $y=4$ is a line parallel to $x$-axis at a distance of 4 units above it.
Statement-2 (R): The line parallel to $x$-axis at a distance a units above the $x$-axis is given by the equation $y=-a$.
Statement-2 (R): The line parallel to $x$-axis at a distance a units above the $x$-axis is given by the equation $y=-a$.
- AStatement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
- BStatement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
- ✓Statement-1 is true, Statement-2 is false.
- DStatement-1 is false, Statement-2 is true.
Answer: C.
View full solution →Statement-1 (A): The graph of the linear equation $4 x+3 y=24$ mects $x$-axis at (-6,0).
Statement-2 (R): Points on $x$-axis are of the form (a, 0), where a is a variable.
Statement-2 (R): Points on $x$-axis are of the form (a, 0), where a is a variable.
- AStatement-1 and Statement-2 are True; Statement-2 is a correct explanation for Statement-1.
- ✓Statement-1 and Statement-2 are True; Statement-2 is not a correct explanation for Statement-1.
- CStatement-1 is True, Statement-2 is False.
- DStatement-1 is False, Statement-2 is True.
Answer: B.
View full solution →Statement-1 (A): The graph of the linear equation $4 x+3 y=24$ mects $x$-axis at (-6,0).
Statement-2 (R): Points on $x$-axis are of the form (a, 0), where a is a variable.
Statement-2 (R): Points on $x$-axis are of the form (a, 0), where a is a variable.
- AStatement-1 and Statement-2 are True; Statement-2 is a correct explanation for Statement-1.
- BStatement-1 and Statement-2 are True; Statement-2 is not a correct explanation for Statement-1.
- CStatement-1 is True, Statement-2 is False.
- ✓Statement-1 is False, Statement-2 is True.
Answer: D.
View full solution →Statement-1 (A): The graph of the linear equation 2x - y + 18 = 0 meets x-axis at (-9, 0).
Statement-2 (R): Coordinates of points on y-axis are of the form (0, a), where a is a variable.
Statement-2 (R): Coordinates of points on y-axis are of the form (0, a), where a is a variable.
- AStatement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
- ✓Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
- CStatement- 1 is true, Statement-2 is false.
- DStatement- 1 is false, Statement-2 is true.
Answer: B.
View full solution →Write the equation representing y-axis.
Write the equation representing x-axis
Write the equation of a line passing through the point (3, 5) and parallel to x-axis.
Write the equation of a line passing through the point (0, 4) and parallel to x-axis.
Write the equation of a line parallel to y-axis and passing through the point (-3, -7).
Write the equation of a line passing through the point (3, 5) and parallel to x-axis.
Write the equation of a line Passing through the point (0, 4) and parallel to x-axis.
Write the equation of a line parallel to y-axis and passing through the point (-3, -7).
The sum of a two digit number and the number obtained by reversing the order of its digits is 121. lf units and ten's digit of the number are x ard y respectively, then write the linear equation representing the above statement.
The cost of ball pen is Rs. 5 less than half of the cost of fountain pen. Write this statement as a linear equation in two variables.
Write two solutions of the form x = 0, y = a and x = b, y = 0 for the following equations:
5x - 2y = 10
5x - 2y = 10
Write two solutions of the form x = 0, y = a and x = b, y = 0 for the following equations:
-4x + 3y = 12
-4x + 3y = 12
Write two solutions of the form x = 0, y = a and x = b, y = 0 for the following equations:
2x + 3y = 24
2x + 3y = 24
Write two solutions for the following equations:
x = 6y
x = 6y
Write two solutions for the following equations:
$\text{x}+\pi\text{y} = 4 $
View full solution →$\text{x}+\pi\text{y} = 4 $
Draw the graphs of the following linear equations on the same graph paper:
2x + 3y = 12, x - y = 1
Find the coordinates of the vertices of the triangle formed by the two straight lines and the y-axis. Also, find the area of the triangle.
2x + 3y = 12, x - y = 1
Find the coordinates of the vertices of the triangle formed by the two straight lines and the y-axis. Also, find the area of the triangle.
Draw the graph of y = |x|.
Draw the graph of y = |x| + 2.
Draw the graph of the following linear equations in two variables:
y = 2x
y = 2x
Draw the graph of the following linear equations in two variables:
x + y = 4
x + y = 4
Teachers and students of class IX of a school had gone to Nandan Kannan for study tour. After visiting different places of Nandan Kannan, lastly, they visited bird's sanctuary and deer park. Rohan a clever boy and keen observer. He put the question to his friends "How many birds are there and how many deer are there (at particular time) in Nandan Kannan?" Rahul's friend, Nishith gave the correct ansuer us follows:
'Nishith answered that total animals have 1000 eyes and 1400 legs.'
(i) If x and y be the number of birds and deer respectively, what is the equation of total number of eyes?
(a) $x+y=1000$ $\quad$(b) $x+y=500$ $\quad$(c) $x-y=1000$ $\quad$(d) $x-y=500$
(ii) What is the equation of total number of legs?
(a) $2 x+y=70$$\quad$(b) $x+2 y=500$$\quad$(c) $x+2 y=700$$\quad$(d) $2 x-y=500$
(iii) How many birds are there in the Zoo?
(a) 1000 $\quad$(b) 5000 $\quad$(c) 300 $\quad$(d) 200
(iv) How many deer are there in the Zoo?
(a) 500 $\quad$(b) 200 $\quad$(c) 300 $\quad$(d) 700
View full solution →'Nishith answered that total animals have 1000 eyes and 1400 legs.'
(i) If x and y be the number of birds and deer respectively, what is the equation of total number of eyes?
(a) $x+y=1000$ $\quad$(b) $x+y=500$ $\quad$(c) $x-y=1000$ $\quad$(d) $x-y=500$
(ii) What is the equation of total number of legs?
(a) $2 x+y=70$$\quad$(b) $x+2 y=500$$\quad$(c) $x+2 y=700$$\quad$(d) $2 x-y=500$
(iii) How many birds are there in the Zoo?
(a) 1000 $\quad$(b) 5000 $\quad$(c) 300 $\quad$(d) 200
(iv) How many deer are there in the Zoo?
(a) 500 $\quad$(b) 200 $\quad$(c) 300 $\quad$(d) 700
Our excessive dependence on motorized road transport imposes significant economic costs on society. These include congestion, road casualties, physical inactivity and ill health caused by it eg.: obesity. Cycling could substantially reduce these risks, while strengthening local economies in both urban and rural areas, supporting local businesses and boosting the economic productivity.
A bicycle is being lent at fixed charges for the first three days of week and an additional charge of each day thereafter. If fixed charges are ₹ x and per day charges are ₹ y, then based on the above information, answer the following questions:
(i) Form the linear equation, if Mr. Sam paid ₹ 27 for a bicycle kept for 7 days.
(ii) Form the linear equation, if Mr. David paid ₹30 for a bicycle kept for 6 days.
(iii) If fixed charge is ₹ 15, then find the additional charge paid by Mr. Sam for each extra day.
(iv) If per day charge for lending the bicycle is ₹ 3, find the value of fixed charge paid by Mr. David.
A bicycle is being lent at fixed charges for the first three days of week and an additional charge of each day thereafter. If fixed charges are ₹ x and per day charges are ₹ y, then based on the above information, answer the following questions:
(i) Form the linear equation, if Mr. Sam paid ₹ 27 for a bicycle kept for 7 days.
(ii) Form the linear equation, if Mr. David paid ₹30 for a bicycle kept for 6 days.
(iii) If fixed charge is ₹ 15, then find the additional charge paid by Mr. Sam for each extra day.
(iv) If per day charge for lending the bicycle is ₹ 3, find the value of fixed charge paid by Mr. David.
The path of a train A is given by th equation 3x + 4y - 12 = 0 and the path or another train B is given by the equation 6x + 8y - 48 = 0. Represent this situation graphically.
Ravish tells his doughter Aarushi, "Seven years ago, I was seven times as old as you were then. Also, three years from now, I shall be three times as old as you will be".. lf present ages of Aarushi and Ravish are x and y years respectively, represent this situation algebraically as well as graphically.
Draw the graphs of the linear equations 4x - 3y + 4 = 0 and 4x + 3y - 20 = 0. Find the area bounded by these lines and x-axis.
Draw the graph of the equation $\frac{\text{x}}{3}+\frac{\text{y}}{4}=1.$ Also, find the area of the triangle formed by the line and the coordinates axes.
View full solution →Draw the graph of the equation 2x + y = 6. Shade the region bounded by the graph and the coordinate axes. Also, find the area of the shaded region.
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