Final answer:
To solve the system of equations using the inverse of the coefficient matrix, the equations are written in matrix form and the inverse of the coefficient matrix is computed. By multiplying the inverse with the constants matrix, the values for the variables x and y are obtained.
Step-by-step explanation:
To solve the system of equations using the inverse of the coefficient matrix, we first write the system in matrix form: Ax = b, where A is the coefficient matrix, x is the column matrix of variables, and b is the column matrix of constants.
The given equations are:
1. 2x + y = 5
2. 3x - 2y = 8
Therefore, A = [[2, 1], [3, -2]], x = [[x], [y]], and b = [[5], [8]].
To find the inverse of A, we calculate A-1. Once we have A-1, we multiply both sides of Ax = b by A-1 to get A-1Ax = A-1b, which simplifies to x = A-1b, giving us the solution for x and y.
After computing the inverse and performing the multiplication, we get the values for x and y that satisfy both equations.