Final answer:
To find the solution to the system of equations represented by the augmented matrix, use row operations to transform the matrix into row-echelon form. Then, solve for the variables by substituting known values.
Step-by-step explanation:
To find the solution to the system of equations represented by the augmented matrix, we can use row operations to transform the matrix into row-echelon form or reduced row-echelon form. In this case, let's use the row operation of multiplying the first row by 4 and adding it to the second row:
[ -1 2 | -3 ]
[ 4 -5 | 6 ]
This yields the following matrix:
[ -1 2 | -3 ]
[ 0 3 | 3 ]
From this row-echelon form, we can see that the system of equations is:
-x + 2y = -3
3y = 3
By substituting 1 for y in the first equation, we can find the value of x:
-x + 2(1) = -3
-x + 2 = -3
-x = -5
x = 5
Therefore, the solution to the system of equations is x = 5 and y = 1.