Question

Solve the following systems using the inverse of a matrix (35 pts). −7x + 3y = −29 (15 pts) 8x − 4y = 36.

a) x = 3, y = 2
b) x = -2, y = 5
c) x = 5, y = -2
d) x = -3, y = -4

Answer 1

To solve the given system of equations using the inverse of a matrix, we set up the augmented matrix, find its inverse, and then multiply the inverse by the augmented matrix to get the solution.

Step-by-step explanation:

To solve the given system of equations using the inverse of a matrix, we need to set up the augmented matrix and then find its inverse. The augmented matrix for the given system is:

[-7, 3, -29]
[8, -4, 36]

Next, we need to find the inverse of the coefficient matrix [-7, 3; 8, -4]. The inverse of a 2x2 matrix is found by swapping the elements on the main diagonal, changing the sign of the elements off the main diagonal, and dividing each element by the determinant. The determinant of the coefficient matrix is (-7*(-4) - 3*8) = 4.

So, the inverse of the coefficient matrix is: [(-4/4), (-3/4); (8/4), (-7/4)] = [-1, -0.75; 2, -1.75]

Multiplying the inverse matrix by the augmented matrix, we get the solution: [3, 2].