Which of the following pair of linear equations has / have many infinite solutions? A. 9x + 3y + 12 = 0; and 18x + 6y + 24 = 0 B. 2x - 3y = 13; and 7x - 2y = 20 C. x + y = 5; and 2x + 2y = 10 D. 3x + y - 3 = 0; and 2x + 2/3y = 2 Choose the correct answer from the options given below: Option 1: A, C and D only Option 2: A, B and D only Option 3: A, B, C and D Option 4: B, C and D only

Answer: A, C and D only. Solution: Infinite solutions require a_1/a_2 = b_1/b_2 = c_1/c_2. A: all ratios equal 1/2, so infinite. B: 2/7 ≠ -3/-2, so a unique solution. C: all ratios equal 1/2, so infinite. D: multiplying the first by 2/3 gives the second exactly, so infinite. Hence A, C and D only.

Quantitative Reasoning

Linear Equation

Medium

Which of the following pair of linear equations has / have many infinite solutions?

A. $9x + 3y + 12 = 0$ ; and $18x + 6y + 24 = 0$

B. $2x - 3y = 13$ ; and $7x - 2y = 20$

C. $x + y = 5$ ; and $2x + 2y = 10$

D. $3x + y - 3 = 0$ ; and $2x + \dfrac{2}{3}y = 2$

Choose the correct answer from the options given below:

A, C and D only

A, B and D only

A, B, C and D

B, C and D only

✅ Correct Option: 1

Infinite solutions require $\dfrac{a_1}{a_2} = \dfrac{b_1}{b_2} = \dfrac{c_1}{c_2}$ .

A: all ratios equal $1/2$ , so infinite.

B: $2/7 \neq -3/-2$ , so a unique solution.

C: all ratios equal $1/2$ , so infinite.

D: multiplying the first by $2/3$ gives the second exactly, so infinite.

Hence A, C and D only.

2026: 14 May Shift 2

Solve the linear equation for $x$ :

$3x - 7 = 2x + 5$

2022: 8 Aug Shift 1

The value of 'y' in the question $2x + 3y - 7 = 0$ if $x = -3/2$

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:

2025: 26 May Shift 1

The intersection point on the Y- axis of $5x - 3y = 9$ is

2025: 28 May Shift 2

The graphs of px + qy = r, mx + ny = s will be

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

(B) overlapping, if the system has a finite number of solutions.

Which of the statements below is/are incorrect?

2025: 19 May Shift 1

If 2x + 3y = 26 and y - x = 2, then the value of x + y is:

Solution

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