Check whether the pair of linear equations $x + 2y - 4 = 0$ and $2x + 4y - 12 = 0$ is consistent or inconsistent.

Question

Accepted Answer

Given equations are: $x + 2y - 4 = 0$ where $a1 = 1, b1 = 2, c1 = -4$ $2x + 4y - 12 = 0$ where $a2 = 2, b2 = 4, c2 = -12$ 
Comparing ratios of coefficients: $\frac{a1}{a2} = \frac{1}{2}$ $\frac{b1}{b2} = \frac{2}{4} = \frac{1}{2}$ $\frac{c1}{c2} = \frac{-4}{-12} = \frac{1}{3}$ 
Here, we observe that: $$\frac{a1}{a2} = \frac{b1}{b2} 
eq \frac{c1}{c2} \quad \left(	ext{since } \frac{1}{2} = \frac{1}{2} 
eq \frac{1}{3}ight)$$ 
Since this condition corresponds to parallel lines having no solution, the given pair of linear equations is inconsistent.

Pair of Linear Equations in Two Variables

❓ Sibling Questions in this Chapter