Quantitative Reasoning

Linear Equation

Medium

The equations: x + 4y - 3 = 0 and 2x + 8y - 6 = 0 have

a unique solution as x = 1, y = -1

a unique solution as x = -3, y = 0

no solution

infinite solutions

✅ Correct Option: 4

Equation 1: $x + 4y - 3 = 0$

Equation 2: $2x + 8y - 6 = 0$

Multiplying Equation 1 by 2:

$2 \times (x + 4y - 3) = 2 \times 0$

$2x + 8y - 6 = 0$

This is exactly the same as Equation 2.

Both equations represent the same line, just written in different ways.

When two equations represent the same line, every point on that line satisfies both equations.

Since a line contains infinitely many points, there are infinite solutions.

For equations $a_1x + b_1y + c_1 = 0$ and $a_2x + b_2y + c_2 = 0$ :

$\dfrac{a_1}{a_2} = \dfrac{b_1}{b_2} = \dfrac{c_1}{c_2}$ indicates infinite solutions.

For the given equations:

$\dfrac{1}{2} = \dfrac{4}{8} = \dfrac{-3}{-6} = \dfrac{1}{2}$

Therefore, the equations have infinite solutions.

2026: 12 May Shift 2

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

(A) 2x – 2y = 10, 3x – 3y = 15

(B) 3x – y = 7, 6x – 2y = 18

(D) 7x – 3y = 3, 14x – 6y = 8

Choose the correct answer from the options given below:

2026: 18 May Shift 1

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

(A). $7x + y = 5, 14x + 2y = 10$

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

(C). $x - y = 10, 3x - 3y = 16$

(D). $2x - 2y - 2 = 0, 4x - 4y - 5 = 0$

Choose the correct option from the given below:

2022: 24 Aug Shift 1

The total age of P and Q is 18 years more than the total age of Q and R. R is how many years younger than P ?

2025: 27 May Shift 2

The pair of linear equations mx + 2y + 3 = 0 and 3x + 6y + 2 = 0 intersect each other, if

2025: 19 May Shift 1

The sum of digits of a two-digit number is 14 and the difference between the two digits of the number is 2. The product of the two digits of the number 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:

The equations: x + 4y - 3 = 0 and 2x + 8y - 6 = 0 have

Solution

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