Solve Using an Inverse Matrix x-y=8 , 4=x-y

Problem

{[x−y=8],[x−y=4])

Solution

1. Write the system in standard form A*x=B

A=([1,−1],[1,−1])

X=([x],[y])

B=([8],[4])

2. Calculate the determinant of the coefficient matrix A

det(A)=(1)*(−1)−(−1)*(1)

det(A)=−1+1

det(A)=0

3. Determine invertibility based on the determinant.

det(A)=0⇒A(−1)* does not exist

4. Analyze the system for solutions. Since the matrix is singular and the equations x−y=8 and x−y=4 represent parallel lines that never intersect, the system is inconsistent.

Final Answer

No solution

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