How do you solve the following system?: #16x +13y =7, -19x +15y = -2#

2 Answers
Zero Two
Apr 25, 2018

#x = 131/7#

#y = -(2047)/91#

Explanation:

  1. #16x+13y = 7#
  2. #15y - 19x =-2#

In equation 1, make #y# the subject.

#13y = 7-16x -> y = (7-16x)/13#

Inject that into equation 2.

#15((7-16x)/13) - 19x = -2#

Solve for #x#.

#(105-240x)/13 -19x = -2#

#(105-240x)/13 = 19x - 2#

#105 -240x = 247x - 26#

#247x-240x = 105+26#

#7x = 131#

#x = 131/7#

Inject the value #x# into the rearranged equation 1 to calculate the value of #y#.

#y = (7-16(131/7))/13#

#y = -(2047)/91#

Ridinion K.
Apr 25, 2018

#x=131/487#
#y=101/487#

Explanation:

#16x+13y=7#
#-19x+15y=-2#

Multiply top equation by #15# and second linear equation by #13# to make the values of #y# the same so they cancel out when subtracted from each other:

#240x+195y=105#
#-247x+195y=-26#
which gives:
#487x=131# when subtracted from each other.
#x=131/487#

Substitute #x# into first original equation:

#16(131/487)+13y=7#
#(2096/487)+13y=7#
#13y=7-(2096/487)#
#13y=(1313/487)#
#y=((1313/487))/13#
#y=101/487#

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