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The cost of $2$ kg apples and $1$ kg of grapes on a day was found to be ₹ $320$. The cost of $4$ kg apples and $2$ kg grapes was found to be ₹ $600$. If cost of $1$ kg apples and $1$ kg of grapes is $x$ and $y$ respectively, represent the given situation algebraically as a system of equations and check whether the system so obtained is consistent or not.
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$2x + y = 320$
$4x + 2y = 600$
Here, $\frac{a_1}{a_2} = \frac{2}{4} = \frac{1}{2}$, $\frac{b_1}{b_2} = \frac{1}{2}$, $\frac{c_1}{c_2} = \frac{320}{600} = \frac{8}{15}$
As $\frac{a_1}{a_2} = \frac{b_1}{b_2} \neq \frac{c_1}{c_2}$
$\therefore$ System of equations is not consistent.
$4x + 2y = 600$
Here, $\frac{a_1}{a_2} = \frac{2}{4} = \frac{1}{2}$, $\frac{b_1}{b_2} = \frac{1}{2}$, $\frac{c_1}{c_2} = \frac{320}{600} = \frac{8}{15}$
As $\frac{a_1}{a_2} = \frac{b_1}{b_2} \neq \frac{c_1}{c_2}$
$\therefore$ System of equations is not consistent.