How do you solve 9a + 7b = -30, 8b + 5c = 11, -3a + 10c = 73?
I have shown how to find
This is a system of 3 linear equations in 3 unknowns, so the easiest will be to use linear matrix algebra to solve it. (either Gaussian elimination, or the inverse matrix method, or Kramer's Rule).
I will use Kramer's Rule as it is probably the quickest.
First write the system of linear equations in coefficient matrix form :
Now use co-factor expansion along any row or column of your choice to find the determinant of this matrix.
Proceeding along row 1, I get
We now form the 3 matrices by replacing each column vector in the coefficient matrix by the column vector of solutions and find the corresponding determinants in each case.
Proceeding in this fashion, we eventually find b and c. I leave the details as an exercise.