Final answer:
To find a solution to the system of equations, we need to find the reduced row-echelon form of the augmented matrix. After performing row operations, we can read off the values of x, y, and z from the reduced matrix.
Step-by-step explanation:
To find a solution to the system of equations, we need to find the reduced row-echelon form of the augmented matrix for the system.
The augmented matrix for the system of equations is:
[4 -2 -5 -51; 4 -1 -2 -36]
Using row operations, we can perform the following steps to reduce the matrix to its reduced row-echelon form:
Step 1: Divide row 1 by 4: [1 -0.5 -1.25 -12.75; 4 -1 -2 -36]
Step 2: Replace row 2 with row 2 - 4(row 1): [1 -0.5 -1.25 -12.75; 0 1 1 3]
Step 3: Divide row 2 by 1: [1 -0.5 -1.25 -12.75; 0 1 1 3]
This gives us the reduced row-echelon form of the augmented matrix. To find the solution to the system of equations, we can read off the values of x, y, and z from the matrix.
x = -12.75, y = 3, z = 0