What is the solution of the system? Solving using matrices.
{-3x + 2y = 10, -4x + 3y = 2
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.