Solve Using an Inverse Matrix 3x+y=-9 , 6x+2y=6

Problem

{[3*x+y=−9],[6*x+2*y=6])

Solution

1. Write the system in matrix form A*X=B where A is the coefficient matrix, X is the variable column vector, and B is the constant column vector.

A=[[3,1],[6,2]]

X=[[x],[y]]

B=[[−9],[6]]

2. Calculate the determinant of matrix A denoted as det(A) using the formula a*d−b*c

det(A)=(3)*(2)−(1)*(6)

det(A)=6−6

det(A)=0

3. Determine the existence of the inverse matrix A(−1) Since the determinant is 0 the matrix A is singular and does not have an inverse.

det(A)=0⇒A(−1)* does not exist

4. Analyze the system for consistency. Since the inverse matrix method cannot be used and the equations represent parallel lines (6*x+2*y=6 simplifies to 3*x+y=3 which contradicts 3*x+y=−9, the system has no solution.

3*x+y=−9

3*x+y=3

−9≠3

Final Answer

No solution

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