Current Attempt in Progress Solve the following linear system by Gaussian elimination. x_(1)+3x_(2)+4x_(3)=9 -x_(1)-4x_(2)+5x_(3)=9 3x_(1)-7x_(2)+6x_(3)=15

To solve the given system of linear equations using Gaussian elimination, we need to perform a series of row operations on the augmented matrix to reach row-echelon form and then use back-substitution to find the solutions.The system of equations is: First, write the augmented matrix for this system: ### Step 1: Make the element below the first pivot (first column, second row) zero.Add the first row to the second row: Subtract 3 times the first row from the third row: ### Step 2: Make the element below the second pivot (second column, third row) zero.Add 16 times the second row to the third row: ### Step 3: Simplify the third row.Divide the third row by 126: ### Step 4: Back-substitution to find the solution.From the third row, we have: Substitute into the second row: Substitute and into the first row: ### Solution: