The graphs of two linear equations, x + 2y = 15 and 4x + 8y = 13 will be:

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Question

This question was previously asked in

SSC CHSL Exam 2024 Tier-I Official Paper (Held On: 02 Jul, 2024 Shift 1)

Answer 1

Given:

Equation 1: x + 2y = 15

Equation 2: 4x + 8y = 13

Formula used:

Two lines are parallel if the ratios of their coefficients of x and y are equal, but the ratio of their constants is different.

Calculation:

First, compare the coefficients of x:

For Equation 1: Coefficient of x = 1

For Equation 2: Coefficient of x = 4

Ratio of coefficients of x:

Next, compare the coefficients of y:

For Equation 1: Coefficient of y = 2

For Equation 2: Coefficient of y = 8

Ratio of coefficients of y: =

Finally, compare the constants:

For Equation 1: Constant = 15

For Equation 2: Constant = 13

Ratio of constants:

⇒ Since the ratio of coefficients of x and y are equal, but the ratio of constants is different, the lines are parallel.

∴ The correct answer is that the graphs of these two equations are parallel lines.