$x = 2, y = -1$ is a solution of the linear equation:
- ✓$x + 2y = 0$
- B$x + 2y = 4$
- C$2x + y = 0$
- D$2x + y = 5$
Answer: A.
View full solution →Question types
Linear Equations In Two Variables question types
158 questions across 8 question groups — pick any mix to generate a Maths paper with step-by-step answer keys.
158
Questions
8
Question groups
5
Question types
01
M.C.Q
51 Q→02Assertion (A) & Reason (B) MCQ
8 Q→031 Marks Question
37 Q→042 Marks Questions
19 Q→053 Marks Question
19 Q→065 Marks Questions
7 Q→07Case study (4 Marks)
2 Q→084 Marks Questions
15 Q→Sample Questions
Linear Equations In Two Variables questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
If $(a, 4)$ lies on the graph of $3x + y = 10$, then the value of a is:
- A$3$
- B$1$
- ✓$2$
- D$4$
Answer: C.
View full solution →If $(4, 19)$ is a solution of the equation $y = ax + 3$, then $a =$
- A$3$
- ✓$4$
- C$5$
- D$6$
Answer: B.
View full solution →If $(2k - 1, k)$ is a solution of the equation $10x - 9y = 12$, then $k =$
- A$1$
- ✓$2$
- C$3$
- D$4$
Answer: B.
View full solution →The distance between the graph of the equations $x = -3$ and $x = 2$ is:
- A$1$
- B$2$
- C$3$
- ✓$5$
Answer: D.
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): Every point on $y$-axis represents a solution of the equation $x=0$.
Statement-2 (R): Points on $y$-axis are of the form (0, k), where k is a variable.
- ✓Statement-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.
- DStatement-1 is False, Statement-2 is True.
Answer: A.
View full solution →Statement-1 (A): Every point on x-axis represents a solution of the equation y = 0.
Statement-2 (R): Points on x-axis are of the form (k, 0), where k is a variable.
Statement-2 (R): Points on x-axis are of the form (k, 0), where k is a variable.
- ✓Statement-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.
- DStatement-1 is False, Statement-2 is True.
Answer: A.
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 →Write the equation of the line that is parallel to $y$-axis and passing through the point: $(3, 5)$
View full solution →Write the equation of the line that is parallel to $x-$axis and passing through the point: $(0, 3)$
View full solution →Write the following as an equation in two variables: $5\text{x}=\frac{7}{ 2}$
View full solution →Write the equation of the line that is parallel to $x-$axis and passing through the point: $(2, -5)$
View full solution →Express the following linear equations in the form $ax + by + c = 0$ and indicate the values of $a, b$ and $c$ in case: $3x = -7y$
View full solution →Solve the equation $3x + 2 = x - 8$, and represent the solution on: The Cartesian plane.
View full solution →Find the value of $\lambda$ if $\text{x}=-\lambda$ and $\text{y} = \frac{5}{2}$ is a solution of the equation $x + 4y - 7 = 0$
View full solution →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.
View full solution →A number is $27$ more than the number obtained by reversing its digits. If its unit's and ten's digit are $x$ and $y$ respectively, write the linear equation representing the above statement.
View full solution →Check the following are solutions of the equation $2x - y = 6$ and which are not: $(2, -2)$
View full solution →Solve the equation $2y - 1 = y + 1$ and represent it graphically on the coordinate plane.
View full solution →Write two solutions of the form x = 0, y = a and x = b, y = 0 for the following equations: 5x - 2y = 10
Give the geometric representations of the following equations:
$a.$ On the number line.
$b.$ On the Cartesain plane.
$2x + 9 = 0$
View full solution →$a.$ On the number line.
$b.$ On the Cartesain plane.
$2x + 9 = 0$
Give the geometrical representation of $2x + 13 = 0$ as an equation in: One variable.
View full solution →Write two solutions of the form $x = 0, y = a$ and $x = b, y = 0$ for the following equations: $-4x + 3y = 12$
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.
View full solution →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 $2x + 3y = 12.$ From the graph, find the coordinates of the point:
$i.$ Whose $y-$coordinates is $3.$
$ii.$ whose $x-$coordinates is $-3.$
View full solution →$i.$ Whose $y-$coordinates is $3.$
$ii.$ whose $x-$coordinates is $-3.$
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.
View full solution →Aarushi was driving a car with uniform speed of $60\ km/ h.$ Draw distance$-$time graph. From the graph, find the distance travelled by Aarushi in:
$i. 2\frac{1}{2}$ Hours
$ii. \frac{1}{2}$ Hour
View full solution →$i. 2\frac{1}{2}$ Hours
$ii. \frac{1}{2}$ Hour
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.
Draw the graph of $y = |x|$.
View full solution →Draw the graph of the following linear equations in two variables: $x + y = 4$
View full solution →Draw the graph of the following linear equations in two variables: $y = 2x$
View full solution →Draw the graph of the equations given below. Also, find the coordinates of the points where the graph cuts the coordinate axes: $3x + 2y + 6 = 0$
View full solution →Draw the graph of the equations given below. Also, find the coordinates of the points where the graph cuts the coordinate axes: $6x - 3y = 12$
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