To solve the system of linear equations using the row echelon method, we start by writing the augmented matrix:
[4 -3 11 | 0]
[3 7 -1 | 0]
We want to eliminate the x-coefficient in the second row. To do this, we subtract 3/4 times the first row from the second row:
[4 -3 11 | 0]
[0 25/4 -25/4 | 0]
Next, we want to eliminate the y-coefficient in the first row. To do this, we add 3/4 times the second row to the first row:
[4 0 1 | 0]
[0 25/4 -25/4 | 0]
Now we have a triangular matrix, which we can solve by back substitution. From the second row, we get:
25/4*y = 25/4
y = 1
Substituting y = 1 into the first row, we get:
4x = -1
x = -1/4
Therefore, the solution to the system of linear equations is:
x = -1/4, y = 1.