\( \left. \begin{array} { l } { ( x - 4 ) ^ { 2 } = } \\ { ( 2 x + 3 ) ^ { 2 } = } \end{array} \right. \)

Solve the system of equations by following steps: - step0: Solution: \(\left\{ \begin{array}{l}\left(x-4\right)^{2}=0\\\left(2x+3\right)^{2}=0\end{array}\right.\) - step1: Calculate: \(\left\{ \begin{array}{l}x=4\\x=-\frac{3}{2}\end{array}\right.\) - step2: Find the intersection: \(x \in \varnothing \) The system of equations given is: 1. \( (x - 4)^{2} = 0 \) 2. \( (2x + 3)^{2} = 0 \) Let's analyze each equation step by step. ### Step 1: Solve the first equation The first equation can be simplified as follows: \[ (x - 4)^{2} = 0 \] Taking the square root of both sides gives: \[ x - 4 = 0 \] Thus, we find: \[ x = 4 \] ### Step 2: Solve the second equation Now, let's solve the second equation: \[ (2x + 3)^{2} = 0 \] Taking the square root of both sides gives: \[ 2x + 3 = 0 \] Solving for \(x\): \[ 2x = -3 \implies x = -\frac{3}{2} \] ### Step 3: Combine the results The solutions we found are: - From the first equation: \( x = 4 \) - From the second equation: \( x = -\frac{3}{2} \) However, since these two values of \(x\) do not satisfy both equations simultaneously, the system has no common solution. ### Conclusion The result of the system of equations is: \[ x \in \varnothing \] This means there are no values of \(x\) that satisfy both equations at the same time.