Algebra
# System of Linear Equations

\[\large{ \begin{cases} 5a+3b+c=17 \\ 1a + 4b+7c=21 \end{cases}} \]

Given that \(a,b\) and \(c\) satisfy the system of equations above, and \(a+b+c\) is equal to \( \dfrac xy \), where \(x\) and \(y\) are coprime positive integers, find \(x+y\).

Which of the following options will not balance any of the other options?

Note that there are 5 options (not 4).

I filled up a \( 3 \times 3 \) grid with numbers, such that if we pick any 2 (not necessarily consecutive) rows and columns, the sum of the 4 numbers in their intersection is equal to 0.

Which is the most specific/restrictive sentence that we say about the numbers in the grid?

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