How do you solve the following system: #4x+3y= -1 , 4x-5y-23=0 #?

2 Answers
EZ as pi
Aug 2, 2018

#x=-5/32 and y = -1/8#

Explanation:

The #x# terms are the same in both equations.

If you subtract the two equations the #x# terms will be eliminated.

#color(white)(xxxxxxx) 4x+3y =-1" "...A#
#color(white)(xxxxxxx) 4x-5y =" "0" "...B#

#A-B:color(white)(xxxxxx)8y = -1#
#color(white)(xxxxxxxxxxxx)y = -1/8#

#color(white)(xxx) 4x +3(-1/8) = -1#

#color(white)(xxxxxxxx) 4x -3/8 = -1#
#color(white)(xxxxxxxxxxx) 4x = -1+3/8#
#color(white)(xxxxxxxxxxx) 4x = -5/8#
#color(white)(xxxxxxxxxxxx) x = -5/32#

Check in #B#

#4(-5/32) -5(-1/8)#

#-5/8 +5/8#

#=0#

Cem Sentin
Aug 3, 2018

#x=2# and #y=-3#

Explanation:

#(4x+3y)-(4x-5y)=-1-23#

#8y=-24#, so #y=(-24)/8=-3#

Hence,

#4x+3*(-3)=-1#

#4x-9=-1#

#4x=8#, thus #x=8/4=2#

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