How do you solve #9x-5y=-44# and #4x-3y=-18# using matrices?
The answer (in matrix form) is:
We can translate the given equations into matrix notation by transcribing the coefficients to elements of a 2x3 matrix:
Divide the second row by 4 to get a one in the "x column."
Add -9 times the second row to the top row to get a zero in the "x column." We'll also revert the second row back to its previous form by multiplying by 4 again.
Multiply the top row by
We now have an answer for y. In order to solve for x, we add 3 times the first row to the second row.
Then divide the second row by 4.
And we finish by reversing the rows since it's traditional to show your final solution in the form of an identity matrix and an auxiliary column.
This is equivalent to the set of equations: