24 ### Solving Systems of Equations using Gaussian Elimination#### Problem Statement**Objective:**Use Gaussian elimination to find the complete solution to the following system of equations, or show that none exists.\[ \begin{cases} 5x_1 + 12x_2 + 5x_3 = 14 \\2x_1 + 5x_2 + 4x_3 = -2 \\x_1 + 2x_2 - 3x_3 = 8 \end{cases} \]#### ChoicesSelect the correct choice below and, if necessary, fill in the answer box(es) to complete your choice.- **A.** The unique solution is \( x_1 = \_\_, x_2 = \_\_, \) and \( x_3 = \_\_ \).- **B.** The system has infinitely many solutions. The solution is \( x_1 = \_\_, x_2 = \_\_, \) and \( x_3 = t \).(Simplify your answer. Type an expression using \( t \) as the variable.)- **C.** The system has infinitely many solutions. The solution is \( x_1 = \_\_, x_2 = s, \) and \( x_3 = t \).(Simplify your answer. Type an expression using \( s \) and \( t \) as the variables.)- **D.** There is no solution.---### Solution ExplanationTo solve this system using Gaussian elimination, perform the following steps:1. **Write the augmented matrix:**\[\begin{pmatrix}5 & 12 & 5 & | & 14 \\2 & 5 & 4 & | & -2 \\1 & 2 & -3 & | & 8 \end{pmatrix}\]2. **Use row operations to achieve row echelon form.**3. **Simplify to reduced row echelon form if needed.**4. **Interpret the resulting matrix to identify the solutions or determine if no solution exists.**---This material guides students through Gaussian elimination, allowing for practical application and better understanding of linear algebra concepts.

Use Gaussian elimination to find the complete solution to the following system of equations, or show that none exists. 5x₁ + 12x₂ + 5x3 = 14 2x₁ + 5x2 + 4x3 = -2 X₁ + 2x2 - 3x3 = 8 Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. A. The unique solution is x₁ = ₁ × ₂ = 1 and X3 = 3 B. The system has infinitely many solutions. The solution is x₁ = , X₂ =, and x₂ = t. (Simplify your answer. Type an expression using t as the variable.) C. The system has infinitely many solutions. The solution is x₁ = x₂ = S, and x3 = t. (Simplify your answer. Type an expression using s and t as the variables.) D. There is no solution.