The pair of linear equations $5x+4y=20$ and $10x+8y=16$, will have no solution. why?

Given: The pair of linear equations $5x+4y=20$ and $10x+8y=16$ will have no solution.

To do:  To explain the reason why the given pair of linear equation has no solution.

Solution:

Here, $a_1=5,\ b_1=4,\ c_1=20$ and $a_2=10,\ b_2=8,\ c_2=16$.

$\frac{a_1}{a_2}=\frac{5}{10}=\frac{1}{2}$

$\frac{b_1}{b_2}=\frac{4}{8}=\frac{1}{2}$

$\frac{c_1}{c_2}=\frac{20}{16}=\frac{5}{4}$

Therefore, we find that $\frac{a_1}{a_2}=\frac{b_1}{b_2}≠\frac{c_1}{c_2}$

Thus, There is no solution for the given pair of equation.

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Updated on: 10-Oct-2022

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