Solve Using an Inverse Matrix 20=8y+11x , 11x+8y=79

Problem

{[20=8*y+11*x],[11*x+8*y=79])

Solution

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

11*x+8*y=20

11*x+8*y=79

2. Represent the system as a matrix equation A*X=B where A is the coefficient matrix, X is the variable matrix, and B is the constant matrix.

A=[[11,8],[11,8]]

X=[[x],[y]]

B=[[20],[79]]

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

det(A)=(11)*(8)−(8)*(11)

det(A)=88−88

det(A)=0

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

det(A)=0⇒A(−1)* does not exist

5. Analyze the consistency of the system. The equations 11*x+8*y=20 and 11*x+8*y=79 represent parallel lines because they have the same coefficients but different constants.

20≠79

Final Answer

No solution

Want more problems? Check here!