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.

Question

x+4y= -15

5x+3y+10

Answer 1

YES, he does!!!

1 4

5 3

has determinant: 1*3-5*4 = 3-20 = -17

so the inverse is

(-1/17) times the matrix

3 -4

-5 1

which is:

-3/17 4/17

5/17 -1/17

Check: 1 4 -3/17 4/17

5 3 5/17 -1/17

does produce the indentity

So

-3/17 4/17 -15

5/17 -1/17 10

gives the solution:

45/17 + 40/17 = 85/17 = 5

-75/17 -19/17 = -85/17 = -5

So x=5 and y = -5