(9) Which statement is true of the system of equations shown below?
\[
\begin{array}{l}
3 x+7 y=14 \\
3 x+7 y=10
\end{array}
\]
(A) The system of equations has one solution: \( (0,4) \)
(B) The system of equations has one solution: \( (4,0) \)
(C) The system of equations has infinite solutions
(D) The system of equations has no solutions

Answer

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Answer

This result is a contradiction, so the system has no solutions

Steps

Step 1 ：Compare two equations: \(3x + 7y = 14\) and \(3x + 7y = 10\)

Step 2 ：Subtract the second equation from the first equation: \(0 = 4\)

Step 3 ：This result is a contradiction, so the system has no solutions