The system $$\left( \begin{array} { l }
2 x + 5 y = 6 \
2 x + 5 y = - 6
\end{array} \right)$$ has the null set for its solution.

Name: The system \[\left( \begin{array} { l } 2 x + 5 y = 6 \\ 2 x + 5 y = - 6 \end{array} \right)\] has the null set for its solution.
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Question

The system $$\left( \begin{array} { l } 
2 x + 5 y = 6 \
2 x + 5 y = - 6
\end{array} \right)$$ has the null set for its solution.

Quizplus · Accepted Answer

Since the two equations have the same coefficients for $x$ and $y$, subtracting one equation from the other yields $0=-12$, which is impossible. Therefore, the system has no solution, or a null set.

The System (2x+5y=62x+5y=−6)\left( \begin{array} { l } 2 x + 5 y = 6 \\2 x + 5 y = - 6\end{array} \right)(2x+5y=62x+5y=−6​)

The System $\left( \begin{array} { l } 2 x + 5 y = 6 \\2 x + 5 y = - 6\end{array} \right)$