Question

The graphic representation of the equations x + 2y = 3 and 2x + 4y + 7 = 0 gives a pair of

Options

• parallel lines

• intersecting lines

• coincident lines

• none of these

Answer 1

Parallel lines

Explanation:

1. Express standard forms

Convert both linear equations into the standard form a_ix + b_iy + c_i = 0:

Equation 1: x + 2y – 3 = 0

Here, a₁ = 1, b₁ = 2 and c₁ = –3.

Equation 2: 2x + 4y + 7 = 0

Here, a₂ = 2, b₂ = 4 and c₂ = 7.

2. Compare the coefficients

We find the ratios of the coefficients of x, y and the constant terms:

`(a_1)/(a_2) = 1/2`

`(b_1)/(b_2) = 2/4 = 1/2`

`(c_1)/(c_2) = (-3)/7`

Since `(a_1)/(a_2) = (b_1)/(b_2) ≠ (c_1)/(c_2)`, the given lines have the same slope but different intercepts. This satisfies the condition for a pair of parallel lines.