How do you solve the following system: # 8x-7y=-39, 5x-9y=-23 #?

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Answer 1 · 2017-07-04T15:56:12

#x = -190/37 and y = -11/37#

Be sure to work with fractions, not decimals which will be recurring and will require rounding, leading to inaccurate answers.

The ideal scenario is to have the numerical coefficients of one of the variables as additive inverses.

#" "color(blue)(8)x-7y =-39" "............................A#
#" "color(red)(5)x-9y=-23" "............................B#

#A xx 5" "color(blue)(40)x-35y =-195" "............................C#
#B xx "-"8" "color(red)("-"40)x+72y =+184" "............................D#

Add the equations:

#C+D:" "37y = -11" "larr x# is eliminated

#color(white)(...............................)y = -11/37#

Now substitute the value for #y# into one of the equations

In #A:" "8x-7(-11/37) =-39#

#8x +77/37 = -39#

#8x = -39-77/37#

#8x = -39-2 3/37#

#8x = -41 3/37#

#8x = -1520/37#

#x =-1520/(8xx37)#

#x = -190/37#

Who comes up with these equations???