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

1 Answer
Jul 4, 2017

Answer:

#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.

Explanation:

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???