23 ### Gauss-Jordan Elimination Method for Systems of Linear EquationsIn this lesson, we will use the Gauss-Jordan elimination method to find all solutions of the systems of equations given below.\[ \begin{align*}4x_1 + 3x_2 &= 26 \\-3x_1 + 3x_2 &= -9 \\6x_1 - 27x_2 &= -24 \\\end{align*} \]#### Write the System as an Augmented MatrixTo begin, we convert the system of equations into an augmented matrix. This is done by writing the coefficients of \(x_1\) and \(x_2\), along with the constants on the right-hand side of the equations, compactly into a matrix form.\[ \left[ \begin{array}{ccc|c}4 & 3 & & 26 \\-3 & 3 & & -9 \\6 & -27 & & -24 \\\end{array} \right] \]#### Solve the SystemNext, we solve the system using the Gauss-Jordan elimination method. Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice:- **Option A:** The unique solution is \(x_1 = \boxed{\phantom{x}}\) and \(x_2 = \boxed{\phantom{x}}\). (Simplify your answers.)- **Option B:** The system has infinitely many solutions. The solution is \(x_1 = \boxed{\phantom{x}}\) and \(x_2 = t\). (Simplify your answer. Type an expression using \(t\) as the variable.)- **Option C:** There is no solution.### ConclusionAfter filling in the above steps, you will determine the correct answer based on the row operations applied to the augmented matrix. The final reduced row echelon form (RREF) of the matrix will reveal whether the system has a unique solution, infinitely many solutions, or no solution at all.

First we will write the given system of equation as a augmented matrix than by using gauss Jordan…

Use the Gauss-Jordan elimination method to find all solutions of the systems of equations. 4x₁ + 3x₂ = 26 - 3x1 + 3x₂ = -9 6x₁27x2 = -24 C Write the system of equations as an augmented matrix. 4 3 26 -3 3 9 6 - 27 - 24 Solve the system. Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. A. The unique solution is x₁ = and X₂ = (Simplify your answers.) = B. The system has infinitely many solutions. The solution is x₁ and x₂ = t. (Simplify your answer. Type an expression using t as the variable.) C. There is no solution.