How do I use Cramer's rule to solve the system of equations #3x+4y=19# and #2x-y=9#?

1 Answer
Mar 1, 2015

The answer is:

#x=5#
#y=1#.

Remembering that the derminant of a matrix #2xx2#,

#a# #b#
#c# #d#

is: #Delta=ad-bc#

First of all let's write the matrix of the coefficients:

#3# #4#
#2# #-1#

and let's find the determinant: #Delta=3*(-1)-2*4=-3-8=-11#, that is not zero, so the system is possible.

Now let's find #Delta_x#, that is the determinant of the previous matrix, in which we have to substitue the column #x# (the first) with the coloumn of the known terms:

#19# #4#
#9# #-1#

so: #Delta_x=19*(-1)-9*4=-19-36=-55#.

And now the same thing with the second column:

#3# #19#
#2# #9#

so: #Delta_y=3*9-2*19=27-38=-11#.

And now the solution is:

#x=Delta_x/Delta=(-55)/-11=5#

#y=Delta_y/Delta=(-11)/-11=1#.