Solve Using an Inverse Matrix 2x+y=8 , 4x+2y=24

Problem

{[2*x+y=8],[4*x+2*y=24])

Solution

1. Write the system of equations in matrix form A*X=B

A=[[2,1],[4,2]]

X=[[x],[y]]

B=[[8],[24]]

2. Calculate the determinant of the coefficient matrix A

det(A)=(2)*(2)−(1)*(4)

det(A)=4−4

det(A)=0

3. Determine if the inverse matrix A(−1) exists.

det(A)=0⇒A(−1)* does not exist

4. Analyze the consistency of the system. Since the determinant is zero, the lines are either parallel or coincident.

2/4=1/2≠8/24

1/2=1/2≠1/3

5. Conclude that because the ratios of the coefficients are equal but the ratio of the constants is different, the lines are parallel and never intersect.

Final Answer

No solution (The system is inconsistent)

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