Final answer:
To solve the system of equations by finding the inverse of the coefficient matrix, rewrite the equations as a matrix equation, find the inverse of the coefficient matrix, multiply the inverse matrix by the variable matrix, and solve for the variables.
Step-by-step explanation:
To solve the system of equations by finding the inverse of the coefficient matrix, we can rewrite the system of equations as:
-4x - y = -5
-x + 3y = -1
Next, we can represent the system of equations as a matrix equation:
| -4 -1 | | x | | -5 || -1 3 | x | y | = | -1 |
Let's call the coefficient matrix A and the variable matrix X:
| -4 -1 | | x || -1 3 | | y |
The inverse of matrix A is found by dividing its adjoint by its determinant. We can then multiply both sides of the equation by the inverse matrix to isolate X:
X = A^(-1) * B
After performing the matrix calculations, we find that the solution to the system of equations is:
x = -4/5
y = -7/5