Quantitative Reasoning

Linear Equation

Medium

The graphs of ax+by = c and dx+ey = f will be:

(A) parallel, if the system has no solution.

(B) coincident, if the system has finite numbers of solutions.

(C) intersecting, if the system has only one solution.

Which of the above statements is/ are correct?

Choose the correct answer from the options given below:

(A) and (B) only

(B) and (C) only

(A), (B) and (C) only

✅ Correct Option: 3

When two linear equations are graphed, their lines can relate in three ways:

Intersecting lines meet at exactly one point, giving one solution
Parallel lines never meet, giving no solution
Coincident lines overlap completely, giving infinite solutions

For statement (A): Parallel lines have no solution

Two lines with the same slope but different positions never intersect.

Example: $x + y = 5$ and $x + y = 10$ have the same slope but never meet.

Statement (A) is correct.

For statement (B): Coincident lines have finite number of solutions

Two coincident lines are the same line, overlapping completely.

Example: $2x + 3y = 6$ and $4x + 6y = 12$ represent the same line.

Every point on the line is a solution, giving infinite solutions, not finite.

Statement (B) is incorrect.

For statement (C): Intersecting lines have only one solution

Two lines with different slopes cross at exactly one point.

Example: $x + y = 5$ and $x - y = 1$ meet at point $(3, 2)$ .

Statement (C) is correct.

Statements (A) and (C) only are correct.

2025: 3 June Shift 1

Read the information given below carefully and answer the question that follows:

Aditi, a salesgirl is appointed at a basic salary of ₹ 1200 per month. The condition of employment further stated that for every sale of ₹ 10000 or above she does, she will get 50 % of basic salary and 10 % of the sales as special incentive. However, this incentive scheme shall not work on the first ₹ 10000 of sales made. What should be the value of sales if Aditi wants to earn ₹ 7600 in a particular month?

2025: 13 May Shift 1

The present age of a father is 4 years more than double the age of his son. After 10 years, the father's age is 30 years more than his son. Then the present age of father is:

2026: 21 May Shift 1

Which one of the following pairs of linear equations is/are inconsistent?

(A) 7 x + 2 y = 3, 14 x + 4 y = 5

(B) 2 x - 3 y = 7, 4 x - 6 y = 12

(D) 2 x - 2 y = 2, 4 x - 4 y = 5

Choose the correct answer from the options given below:

2024

The present age of Harish is 8 times the sum of the ages of his two sons at present. After 8 years, his age will be 2 times the sum of the ages of his two sons. The present age of Harish (in years) is:

2026: 20 May Shift 2

Which of the following pairs of linear equations is/are consistent?

A. x + y – 5 = 0, 3x + 2y – 10 = 0

B. 3x – 2y – 6 = 0, 6x – 4y – 12 = 0

C. x – y – 9 = 0, 3x – 3y – 27 = 0

D. x + y – 4 = 0 , 3x + 3y – 12 = 0

Choose the correct option from the given below:

2023: 1 June Shift 1

Linear equations $3x + 5y = 19$ and $10x - 3y = 24$ have solution $x = \frac{\alpha}{3}$ and $y = \frac{\beta}{2}$ , then the value of $\alpha + \beta$ is:

Solution

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