NCERT · Class 10 · Mathematics · Pair of Linear Equations in Two VariablesCheck whether the pair of linear equations $x + 2y - 4 = 0$ and $2x + 4y - 12 = 0$ is consistent or inconsistent.

Given equations are:

1. $x + 2y - 4 = 0$ where $a_1 = 1, b_1 = 2, c_1 = -4$
2. $2x + 4y - 12 = 0$ where $a_2 = 2, b_2 = 4, c_2 = -12$ \nComparing ratios of coefficients:

• $\frac{a_1}{a_2} = \frac{1}{2}$
• $\frac{b_1}{b_2} = \frac{2}{4} = \frac{1}{2}$
• $\frac{c_1}{c_2} = \frac{-4}{-12} = \frac{1}{3}$ \nHere, we observe that: $$\frac{a_1}{a_2} = \frac{b_1}{b_2} \neq \frac{c_1}{c_2} \quad \left(\text{since } \frac{1}{2} = \frac{1}{2} \neq \frac{1}{3}\right)$$ \nSince this condition corresponds to parallel lines having no solution, the given pair of linear equations is inconsistent.