Solve Using an Inverse Matrix y=1/3x+2 , y=1/3x+3

Problem

{[y=1/3*x+2],[y=1/3*x+3])

Solution

1. Rearrange the equations into standard form A*x+B*y=C by subtracting 1/3*x from both sides of each equation.

−1/3*x+y=2

−1/3*x+y=3

2. Write the system as a matrix equation in the form A*x=b

[[−1/3,1],[−1/3,1]]*[[x],[y]]=[[2],[3]]

3. Calculate the determinant of the coefficient matrix A using the formula det(A)=a*d−b*c

det(A)=(−1/3)*(1)−(1)*(−1/3)

det(A)=−1/3+1/3=0

4. Determine the existence of an inverse. Since the determinant is 0 the matrix A is singular and does not have an inverse.

5. Analyze the system. Because the lines have the same slope (1/3 but different y-intercepts (2 and 3, the lines are parallel and never intersect.

Final Answer

No solution

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