Question

Solve the system of equations by finding the inverse of the coefficient matrix. −4x−y=−5, 3y−x=−1

A) x=−3,y=1

B) x=−1,y=3

C) x=1,y=−3

D) x=3,y=−1

Answer 1

To solve the system, we find the inverse of the coefficient matrix and multiply it by the constants matrix. After performing the calcultion, the solution to the system is x = -1, y = 3.

Step-by-step explanation:

To solve the system of equations by finding the inverse of the coefficient matrix, we first write the system of equations in matrix form:

Let's define the matrix A as the coefficient matrix, X as the column matrix of variables, and B as the column matrix of constants:

• Matrix A: [[-4, -1], [-1, 3]]
• Matrix X: [x, y]
• Matrix B: [-5, -1]

The matrix equation is A * X = B, and to find X, we multiply both sides by the inverse of A, so X = A-1 * B.

First, calculate the inverse of A (A-1). Then, multiply A-1 by B to find the values of x and y. After calcultion, we find:

x = -1 and y = 3

Therefore, the correct answer is B) x = -1, y = 3.