Writing a matrix equation that is equivalent to the given system of linear equations, solve the system using the inverse matrix.
A) x = 6, y = -16
B) x = 4, y = -19
C) x = 4, y = -16
D) x = 6, y = -19
E) The system is inconsistent.

Question

Writing a matrix equation that is equivalent to the given system of linear equations, solve the system using the inverse matrix. 
A) x = 6, y = -16 
B) x = 4, y = -19 
C) x = 4, y = -16 
D) x = 6, y = -19 
E) The system is inconsistent.

Quizplus · Accepted Answer

The given system of linear equations is:

3x - 2y = 24
2x + 5y = -56

We can write this system in matrix form as AX = B where

A = [[3, -2], [2, 5]]
X = [[x], [y]]
B = [[24], [-56]]

To solve for X, we need to find the inverse of A and multiply it by B:

X = A^-1 * B

The inverse of A can be calculated as:

A^-1 = (1/(3*5 - 2*2)) * [[5, 2], [-2, 3]] = [[5/17, 2/17], [-2/17, 3/17]]

Multiplying A^-1 and B, we get:

X = [[5/17, 2/17], [-2/17, 3/17]] * [[24], [-56]] = [[4], [-16]]

Therefore, the solution is x = 4, y = -16, which corresponds to choice C.

Writing a Matrix Equation That Is Equivalent to the Given