Solve the following system of equations by using the inverse of the coefficient

Question

Solve the following system of equations by using the inverse of the coefficient matrix if it exists and by the echelon method if the inverse doesn't exist. 3x+y=24 14x + 5y = 113 Select the correct choice below and fill in any answer boxes within your choice. A. The solution of the system is (Simplify your answer. Type an ordered pair.) B. There are infinitely many solutions. The solution is where y is any real number. (Simplify your answer. Use integers or fractions for any numbers in the expression.) ° C. There is no solution.

Explanation / Answer

Dear Student Thank you for using Chegg Given equations If Ax = B A = 3 1 B = 24 X = x 14 5 113 y Computing adj(A) a11 = 5 a12 = -14 a21 = -1 a22 = 3 adj(A) = 5 -1 -14 3 det(A) = 1 inv(A) = (1/det(A))* adj(A) = 5 -1 -14 3 X = A ^ -1 * B = 5 -1 * 24 -14 3 113 = 7 3 Hence x =   7 y = 3 is the solution to given set of equations

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