Question

4. Solve the following by MATRIX method
2X+2y =20
10x+4y=10 [3 marks]

Answer 1

To solve this system of equations using the matrix method, we first need to set up the coefficients of the variables x and y in matrix form.

The system of equations can be written as AX = B, where
A = [[2, 2], [10, 4]],
X = [[x], [y]], and
B = [[20], [10]].

Now, in order to solve for X, we need to find the inverse of matrix A and multiply it with matrix B.
First, let's find the determinant of matrix A:
det(A) = 2(4) - 2(10) = 8 - 20 = -12

Next, let's find the inverse of matrix A:
A^-1 = 1/det(A) * adj(A), where adj(A) represents the adjugate matrix of A.
adj(A) = [[4, -2], [-10, 2]]
A^-1 = 1/(-12) * [[4, -2], [-10, 2]]
A^-1 = [[-1/3, 1/6], [5/3, -1/3]]

Now, let's multiply A^-1 with B to find X:
X = A^-1 * B
X = [[-1/3, 1/6], [5/3, -1/3]] * [[20], [10]]
X = [[-1/3 * 20 + 1/6 * 10], [5/3 * 20 - 1/3 * 10]]
X = [[-20/3 + 10/6], [100/3 - 10/3]]
X = [[-20/3 + 5/3], [90/3]]
X = [[-15/3], [30/3]]
X = [[-5], [10]]

Therefore, the solution to the system of equations is x = -5 and y = 10.