To determine whether the two equations form a system with no solution, we should analyze each one.
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First equation: \(2x + 3 = 2x + 7\)
Subtract \(2x\) from both sides:
\[ 3 = 7 \]
This is a false statement, indicating that the first equation has no solutions.
-
Second equation: \(5x + 5 = 5x + 4\)
Subtract \(5x\) from both sides:
\[ 5 = 4 \]
This is also a false statement, indicating that the second equation also has no solutions.
Since both individual equations have no solution, the combined system they form also has no solution. There are infinitely many \(x\) values that do not satisfy either equation.
Thus, the system of equations:
\[ \begin{align*}
- & \quad 2x + 3 = 2x + 7 \
- & \quad 5x + 5 = 5x + 4 \end{align*} \]
forms a system with no solution.