How do you solve using gaussian elimination or gauss-jordan elimination, #10x-20y=-14#, #x +y = 1#?

1 Answer

Answer:

#x=1/5# and #y=4/5#

Explanation:

From the given , take note of the numerical coefficients of #x# and #y# and the constants.

the given

#10x-20y=-14#
#x+y=1#

Arrange in rows. So that first row for the first equation, second row for the second. First column for the coefficients of x, second column for the coefficients of y aand third column for the constants.

#X.......Y.........K#

#10 \ \ -20 \ \ ] \ \ -14#
# 01 \ \ +01 \ \ ] \ \ +01#
~~~~~~~~~~~~~~~~~~

#01 \ \ -02 \ \ ]\ \-7/5# ........this is after dividing row 1 by 10
#01 \ \ +01 \ \ ] \ \ +01#
~~~~~~~~~~~~~~~~~~

#01 \ \ -02 \ \ ]\ \-7/5#
# \ \ 0 \ \ +03 \ \ ] \ \+12/5# .........this is after changing the sign of
~~~~~~~~~~~~~~~~~~~~~ previous row 1 and adding result to row 2

#01 \ \ -02 \ \ ]\ \-7/5#
# \ \ 0 \ \ +01 \ \ ]\ \+4/5# .......this is after dividing previous row 2 by 3
~~~~~~~~~~~~~~~~~~
# \ 01 \ \ +0 \ \ ]\ \+1/5#........this is after multiplying previous row 2
# \ \ 0 \ \ +01 \ \ ]\ \+4/5# # \ \ # # \ \ # by 2 then adding result to row 1.

Take note of the coefficients at this point
#1*x+0*y=1/5#
#0*x+1*y=4/5#

The result #x=1/5#
and also #y=4/5#

Have a nice day !!! from the Philippines.