Determine, whether the system of equations $x-2y=2,\ 4x-2y=5$ is consistent or inconsistent.

Given: System of equations:  $x-2y=2,\ 4x-2y=5$

To do: To determine, whether the given system of equations is consistent or inconsistent.

Solution:

Given system of equations: $x-2y=2,\ 4x-2y=5$

Here, $\frac{a_1}{a_2}=\frac{1}{4}$

$\frac{b_1}{b_2}=\frac{-2}{-2}=1$

We find that, $\frac{a_1}{a_2}≠\frac{b_1}{b_2}$

Therefore, the given system of equations have one unique solution.

Thus, the given system of equations is consistent.

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Updated on: 10-Oct-2022

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