Question

check the given pair of equations are consistent or inconsistent x-2y=5 and 2x-4y=1.​

Answer 1

inconsistent

Step-by-step explanation:

x - 2y = 5

=> x - 2y - 5 = 0.....(1)

2x - 4y = 1

=> 2x - 4y - 1 = 0.....(2)

In the standard form of linear equation of two variables, here -

$a_{1} = 1 \: . \: b_{1} = - 2 \: . \: c_{1} = - 5 \\ a_{2} = 2 \: . \: b_{2} = - 4 \: . \: c_{2} = - 1$

So,

$\frac{a_{1}}{a_{2}} = \frac{1}{2} \\ \frac{b_{1}}{b_{2}} = \frac{ - 2}{ - 4} = \frac{1}{2} \\ \frac{c_{1}}{c_{2}} = \frac{ - 5}{ - 1}$

$= > \frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} \neq \frac{c_{1}}{c_{2}}$

So,

there will be no zero for this pair of equation.

And The pairs are inconsistent.

Hope it helps.

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