Answer: To solve the system of equations using the matrix method, we first need to set up the corresponding coefficient matrix and augmented matrix:
Coefficient matrix:
[1 4]
[2 -3]
Augmented matrix:
[1 4 | 9]
[2 -3 | 7]
To solve the system using matrix method, we perform row operations on the augmented matrix to get it into row echelon form, and then back substitute to obtain the solutions.
Performing row operations:
Multiply the first row by 2 and subtract the result from the second row:
[1 4 | 9]
[0 -11| -11]
Divide the second row by -11:
[1 4 | 9]
[0 1 | 1]
Subtract 4 times the second row from the first row:
[1 0 | 5]
[0 1 | 1]
The row echelon form of the augmented matrix is:
[1 0 | 5]
[0 1 | 1]
Therefore, the solution is x = 5 and y = 1.
So the solution of the system of equations is x = 5 and y = 1.
Explanation: