How do you solve #9x-5y=-44# and #4x-3y=-18# using matrices?

1 Answer
Jul 10, 2016

Answer:

The answer (in matrix form) is: #((1,0, -6),(0,1, 2))#.

Explanation:

We can translate the given equations into matrix notation by transcribing the coefficients to elements of a 2x3 matrix:

#((9, -5, -44), (4, -3, -18))#

Divide the second row by 4 to get a one in the "x column."

#((9, -5, -44), (1, -3/4, -9/2))#

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.

#((0, 7/4, -7/2), (4, -3, -18))#

Multiply the top row by #4/7# to get a 1 in the "y column."

#((0, 1, -2), (4, -3, -18))#

We now have an answer for y. In order to solve for x, we add 3 times the first row to the second row.

#((0, 1, -2), (4, 0, -24))#

Then divide the second row by 4.

#((0, 1, -2), (1, 0, -6))#

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.

#((1, 0, -6), (0, 1, -2))#

This is equivalent to the set of equations:
#x = -6#
#y = -2#