How do you solve the following system?: #-13x -3y =6, 8x -y = -1#

1 Answer
Alan P.
Nov 19, 2015

#(x,y) = (-9/37,35/37)#
(see below for method of solution)

Explanation:

Given
[1]#color(white)("XXX")-13x-3y=6#
[2]#color(white)("XXX")8x-y=-1#

Multiply [2] by 3 (to give #y# the same coefficient as in [1])
[3]#color(white)("XXX")24x-3y=-3#

Subtract [1] from [3] (to get rid of the #y# term)
[4]#color(white)("XXX")37x=-9#

Divide [4] by 27
[5]#color(white)("XXX")x=-9/37#

Re-write [2] as an equation for #y# by adding #(y+1)# to both sides and switching the sides
[6]#color(white)("XXX")y=8x+1#

Substitute #(9/37)# from [5] for #x# in [6]
[7]#color(white)("XXX")y=8(-9/37)+1#

Simplify [7]:
[8]#color(white)("XXX")y=-35/37#

Probably the biggest problem here is trusting your calculations (or being willing to do them in the first place) since the answer isn't "pretty".

If it helps a graph can help verify that the answer is within an appropriate range:
graph{(-13x-3y-6)*(8x-y+1)=0 [-3.97, 3.826, -2.976, 0.917]}

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