To determine whether the equations have solutions, let's first analyze each equation and see if both sides are equal when substituting \(x = 2\) and \(x = -3\).
Equation 1:
\[ 2x + 3 = 2x + 7 \]
Substituting \(x = 2\): \[ 2(2) + 3 = 2(2) + 7 \] \[ 4 + 3 = 4 + 7 \] \[ 7 = 11 \quad \text{(not true)} \]
Substituting \(x = -3\): \[ 2(-3) + 3 = 2(-3) + 7 \] \[ -6 + 3 = -6 + 7 \] \[ -3 = 1 \quad \text{(not true)} \]
So for Equation 1, both substitutions do not hold true.
Equation 2:
\[ 5x + 5 = 5x + 4 \]
Substituting \(x = 2\): \[ 5(2) + 5 = 5(2) + 4 \] \[ 10 + 5 = 10 + 4 \] \[ 15 = 14 \quad \text{(not true)} \]
Substituting \(x = -3\): \[ 5(-3) + 5 = 5(-3) + 4 \] \[ -15 + 5 = -15 + 4 \] \[ -10 = -11 \quad \text{(not true)} \]
This means for both substitutions \(x = 2\) and \(x = -3\), Equation 2 is also not true.
Conclusion:
Both equations produce contradictions regardless of whether we substitute \(x = 2\) or \(x = -3\). Therefore, both equations do not have any solutions.
Moreover, we can recognize that both equations represent parallel lines; the first equation simplifies to \(3 \neq 7\) (a contradiction), and the second equation simplifies to \(5 \neq 4\) (another contradiction). Since the equations yield false statements, they do not intersect and hence have no solutions.