Solve Using an Inverse Matrix 2x-2y-3=0 , x-y-10=0

Problem

{[2*x−2*y−3=0],[x−y−10=0])

Solution

1. Rearrange the equations into the standard form a*x+b*y=c

2*x−2*y=3

x−y=10

2. Write the system as a matrix equation A*X=B

[[2,−2],[1,−1]]*[[x],[y]]=[[3],[10]]

3. Calculate the determinant of the coefficient matrix A

det(A)=(2)*(−1)−(−2)*(1)

det(A)=−2+2

det(A)=0

4. Determine if an inverse matrix exists. Since the determinant is zero, the matrix A is singular and does not have an inverse.

5. Analyze the consistency of the system. Divide the first equation 2*x−2*y=3 by 2 to get x−y=1.5 This contradicts the second equation x−y=10

Final Answer

No solution

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