How do you solve the system #4x-y=9# and #x-3y=16#?

1 Answer
Alan P.
Jun 4, 2015

#(x,y)=(1,-5)#

Explanation:

Given
[1]#color(white)("XXXX")##4x-y = 9#
[2]#color(white)("XXXX")##x-3y = 16#

Re-arrange the terms of [2] to get
[3]#color(white)("XXXX")##x = 3y+16#

Using [3] substitute #(3y+16)# for #x# in [1]
[4]#color(white)("XXXX")##4(3y+16)-y = 9#

Simplifying
[5]#color(white)("XXXX")##11y +64 = 9#
[6]#color(white)("XXXX")##11y = -55#
[7]#color(white)("XXXX")##y = -5#

Using [7] substitute #(-5)# for #y# in [1]
[8]#color(white)("XXXX")##4x - (-5) = 9#
[9]#color(white)("XXXX")## 4x = 4#
[10]#color(white)("XXXX")##x = 1#

#(x,y) = (1,-5)#

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