What is the solution of the system? Solving using matrices.

Question

{-3x + 2y = 10, -4x + 3y = 2

Answer 1

To solve this system of linear equations, we can write it in matrix form and perform matrix operations. The system of equations is:

-3x + 2y = 10
-4x + 3y = 2

The coefficient matrix is:
A = [[-3, 2],
[-4, 3]]

The constant matrix is:
B = [[10],
[2]]

The variable matrix is:
X = [[x],
[y]]

The system of equations can be represented as AX = B.

To solve for X, we can multiply both sides of the equation by the inverse of matrix A:
A^-1 * AX = A^-1 * B
X = A^-1 * B

Calculate the inverse of matrix A:
A = [[-3, 2],
[-4, 3]]

The determinant of matrix A is:
det(A) = (-3)*(3) - (-4)*(2) = -9 + 8 = -1

The inverse of matrix A is:
A^-1 = (1/det(A)) * [[3, -2],
[4, -3]]
A^-1 = [[-3, 2],
[-4, 3]]

Therefore, X = A^-1 * B
X = [[-3, 2],
[-4, 3]] * [[10],
[2]]

X = [[-30 + 4],
[-40 + 6]]

X = [[-26],
[-34]]

Therefore, the solution to the system of equations is x = -26 and y = -34.