Final answer:
Solving the given linear equations, will get the values of x and y are x = 16/11 and y = 43/11.
Step-by-step explanation:
To find the values of x and y for the given simultaneous linear equations using the inverse matrix method, we need to represent the equations in matrix form and then find the inverse of the coefficient matrix.
The given equations are:
2x + 3y = -2
5x + 2y = 17
Writing these equations in matrix form, we get:
[2 3] [x] = [-2]
[5 2] [y] [17]
To find the inverse of the coefficient matrix [2 3; 5 2], we calculate the determinant first:
det([2 3; 5 2]) = (2 * 2) - (3 * 5) = -11
The inverse of the coefficient matrix is:
[2 3]^-1 = 1/det * [2 -3] = 1/-11 * [2 -3] = [-2/11 3/11]
[5 2] [-5 2] [-5/11 2/11]
Multiplying the inverse of the coefficient matrix with the constant matrix gives us the values of x and y:
[x] = [2/11 -3/11] [-2] = [-2/11 * 2 - 3/11 * 17] = [16/11 -51/11]
[y] [-5/11 2/11] [17] [-5/11 * 2 + 2/11 * 17] [43/11 16/11]
Therefore, the values of x and y are x = 16/11 and y = 43/11.