Class 10 - Chapter 3: Linear Equations

Section A (1 Mark each)

Q1. The value of $k$ for which the system of equations $x + 2y = 5$ and $3x + ky + 15 = 0$ has no solution is:

(a) -6 (b) 6 (c) 3/2 (d) -3/2

Q2. If a pair of linear equations is consistent, then the lines will be:

(a) intersecting or coincident (b) always coincident (c) parallel (d) always intersecting

Q3. The solution of the equations $x + y = 14$ and $x - y = 4$ is:

(a) $x=5, y=9$ (b) $x=9, y=5$ (c) $x=10, y=4$ (d) $x=9, y=4$

Q4. Assertion (A): The linear equations $x - 2y - 3 = 0$ and $3x - 6y - 9 = 0$ represent coincident lines.
Reason (R): If $\frac{a_1}{a_2} = \frac{b_1}{b_2} = \frac{c_1}{c_2}$, then the lines are coincident.

(a) Both A and R are true and R is the correct explanation of A. (b) Both A and R are true but R is not the correct explanation of A. (c) A is true but R is false. (d) A is false but R is true.

Section B (2 Marks each)

Q5. Solve for $x$ and $y$: $2x + 3y = 11$ and $2x - 4y = -24$.

Solve on white paper.

Q6. Find the value of $k$ for which the pair of linear equations $kx + 3y = k-3$ and $12x + ky = k$ has no solution.

Solve on white paper.

Q7. 5 pencils and 7 pens together cost ₹ 50, whereas 7 pencils and 5 pens together cost ₹ 46. Find the cost of one pencil and that of one pen.

Solve on white paper.

Section C (3 Marks each)

Q8. Solve the following pair of linear equations by the substitution method:
$3x - 5y - 4 = 0$ and $9x = 2y + 7$.

Solve on white paper.

Q9. The sum of a two-digit number and the number obtained by reversing the digits is 66. If the digits of the number differ by 2, find the number. How many such numbers are there?

Solve on white paper.

Section D (5 Marks)

Q10. Solve the following pair of linear equations graphically:
$x - y + 1 = 0$
$3x + 2y - 12 = 0$
Calculate the area bounded by these lines and the x-axis.

Solve on white paper.

Section E (4 Marks)

Q11. Case Study:

A taxi charges in a city consist of a fixed charge together with the charge for the distance covered. For a distance of 10 km, the charge paid is ₹ 105 and for a journey of 15 km, the charge paid is ₹ 155.

(i) Form the pair of linear equations representing the situation.

(ii) Find the fixed charge and the charge per km.

(iii) How much does a person have to pay for travelling a distance of 25 km?

Solve on white paper.