Prove that the following equations inconsistent. $4 x + 6 y = 14, 12 x + 18 y = 32$ .

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Solution

Two lines are said to be inconsistent when they do not intersect.
Hence, it would be sufficient to prove that they are parallel.
Rearranging the equations of the lines,
we have $y = \frac{- 4}{6} x + \frac{14}{6} ⟹ y = \frac{- 2}{3} x + \frac{7}{3}$ and $y = \frac{- 12}{18} x + \frac{32}{18} ⟹ y = \frac{- 2}{3} x + \frac{16}{9}$
On comparing both lines to standard slope form of line ( $y = m x + c$ ), we see that they have the same slope but the constants are different.
Hence, the lines are non-intersecting parallel and hence, inconsistent.

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Prove that the following equations inconsistent. 4x+6y=14,12x+18y=32.

Prove that the following equations inconsistent. $4 x + 6 y = 14, 12 x + 18 y = 32$ .