Is the following pair of linear equations is consistent in solution graph $2x + y - 6 = 0,\ 4x + 2y -4 =0$.
Given: Pair of equations: $2x + y - 6 = 0,\ 4x + 2y -4 =0$.
To do: To find out whether the given pair of equations is consistent or inconsistent.
Solution:
Given equations are: $2x + y - 6 = 0,\ 4x + 2y -4 =0$.
$\frac{a_1}{a_2}=\frac{2}{4}=\frac{1}{2}$
$\frac{b_1}{b_2}=\frac{1}{2}$
$\frac{c_1}{c_2}=\frac{-6}{-4}=\frac{2}{1}$
Here we find, $\frac{a_1}{a_2}=\frac{b_1}{b_2}≠\frac{c_1}{c_2}$
Therefore, these linear equations are parallel to each other and thus have no possible solution.
So, the pair of linear equations is inconsistent.
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