Class 9 Maths: Linear Equation in Two Variables – Extra Questions with Answers
Q. 1 If $\angle C$ and $\angle D$ are complementary angles, and $\angle C$ measures $35^\circ$, what is the measure of $\angle D$ in degrees?
Check Solution
Ans: A
Solution: Complementary angles add up to $90^\circ$.
$90^\circ – 35^\circ = 55^\circ$
Answer: 55
Q. 2 If 3x + 6 = 12, and we divide both sides of the equation by 3, what is the resulting equation?
Check Solution
Ans: A
Solution:
(3x + 6) / 3 = 12 / 3
x + 2 = 4
Answer: x + 2 = 4
Q. 3 Find the point of intersection of the following two lines: $2x + y = 7$ $x = 4y$
Check Solution
Ans: A
Solution:
Substitute $x = 4y$ into the first equation:
$2(4y) + y = 7$
$8y + y = 7$
$9y = 7$
$y = \frac{7}{9}$
Substitute $y = \frac{7}{9}$ into $x = 4y$:
$x = 4(\frac{7}{9})$
$x = \frac{28}{9}$
Answer: $(\frac{28}{9}, \frac{7}{9})$
Q. 4 Which of the following points lies on the line defined by the equation y = 2x + 1? (i) (1, 2) (ii) (2, 5) (iii) (3, 7)
Check Solution
Ans: A
Solution: Substitute the x-coordinate of each point into the equation y = 2x + 1 and check if the resulting y-coordinate matches the point’s y-coordinate.
(i) For (1, 2): y = 2(1) + 1 = 3. Since 3 != 2, (1, 2) does not lie on the line.
(ii) For (2, 5): y = 2(2) + 1 = 5. Since 5 == 5, (2, 5) lies on the line.
(iii) For (3, 7): y = 2(3) + 1 = 7. Since 7 == 7, (3, 7) lies on the line.
Answer: (ii) and (iii)
Q. 5 How many linear equations in $x$ and $y$ can be satisfied by $x = 1$ and $y = 1$?
Check Solution
Ans: C
Solution:
Infinitely many. Any equation of the form $ax + by = a+b$ where a and b are real numbers will be satisfied by $x=1$ and $y=1$.
Answer: Infinitely many
Q. 6 Give the geometric representations of $x = -2$ as an equation: (i) in one variable (ii) in two variables
Check Solution
Ans: C
Solution:
(i) $x = -2$ represents a point on the number line.
(ii) $x = -2$ represents a vertical line in the Cartesian plane.
Answer:
(i) Point at -2 on the number line
(ii) Vertical line passing through (-2, y)
Q. 7 The coordinates of points in the table: | x | 0 | 1 | 2 | 3 | 4 | |—|—|—|—|—|—| | y | 2 | 3 | 4 | 5 | 6 | represent some of the solutions of a linear equation. Determine the y-coordinate when x = 10.
Check Solution
Ans: A
Solution: The points form a linear equation with a slope of 1 and a y-intercept of 2. The equation is y = x + 2. When x = 10, y = 10 + 2 = 12.
Answer: 12
Q. 8 If a linear equation has solutions $(1, 1)$ and $(3, -1)$, then it is of the form _______.
Check Solution
Ans: C
Solution:
First, find the slope: m = (-1 – 1) / (3 – 1) = -2 / 2 = -1.
Then, use point-slope form: y – 1 = -1(x – 1)
Simplify to slope-intercept form: y – 1 = -x + 1 => y = -x + 2.
Answer: y = -x + 2
Q. 9 If the work done by a body on application of a constant force is directly proportional to the distance travelled by the body, express this in the form of an equation in two variables. Then, draw the graph of the same by taking the constant force as 3 units. Also read from the graph the work done when the distance travelled by the body is (i) 4 units and (ii) 0 units.
Check Solution
Ans: C
Solution:
Let W be the work done, and d be the distance travelled.
Since work done is directly proportional to distance, we have W ∝ d
Therefore, W = k * d, where k is the constant force.
Given k = 3 units, so W = 3d
The equation in two variables is W = 3d.
For the graph, plot the points (0,0), (1,3), (2,6), (3,9), (4,12), etc.
(i) When d = 4 units, W = 3 * 4 = 12 units.
(ii) When d = 0 units, W = 3 * 0 = 0 units.
Answer:
W = 3d
(i) 12 units
(ii) 0 units
Q. 10 A and B are siblings. B is younger than A by 3 years. Their mother, M, is twice the age of A. Their father, F, is 7 years older than three times B’s age. If the present age of F is 43 years, then find the present ages of A, B, and M respectively.
Check Solution
Ans: B
Solution:
F = 43
F = 3B + 7
43 = 3B + 7
3B = 36
B = 12
A = B + 3 = 12 + 3 = 15
M = 2A = 2 * 15 = 30
Answer: 15, 12, 30
Next Topic: Inroduction to Euclid’s Geometry
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