Question

Is it true to say that the pair of equations 2x – 4y = 5 and –x + 2y = 7 has a unique solution? Justify your
answer. ​

Answer 1

2x - 4y = 5    ⇒ 2x - 4y - 5 = 0

-x + 2y = 7    ⇒ -x + 2y - 7 = 0

for unique solution,

$\frac{a_1}{a_2} \neq \frac{b_1}{b_2}$

here,

$\frac{a_1}{a_2} = \frac{2}{-1} where, \frac{2}{-1} becomes \frac{-2}{1}$

$\frac{b_1}{b_2} = \frac{-4}{2} where, \frac{-4}{2} becomes \frac{-2}{1}$

as in this case,

$\frac{a_1}{a_2} = \frac{b_1}{b_2}$

so we can say that the solution of the pair of equations is not a unique solution.