How do you solve the following system: #2x - 3y = 10 , 2x + 3y = 12#?

1 Answer
Dec 14, 2015

Answer:

#color(white)(xx)x=11/2#, and #y=1/3#

Explanation:

#color(white)(xx)2x-3y=10,color(white)(x)2x+3y=12#

#color(white)(xx)2x-3y=10<=>3y=2x-10#
#color(white)(xx)2x+3y=12<=>3y=-2x+12#

#=>2x-10=y#
#=>2x-10=color(red)(-2x+12)#

Add #color(red)(+2x+10)# to both side:
#color(white)(xx)2x-10color(red)(+2x+10)=-2x+12color(red)(+2x+10)#
#=>4x=22#

Multiply both sides by #color(red)(1/4)#:
#color(white)(xx)color(red)(1/4xx)4x=color(red)(1/4xx)22#
#=>x=11/2#

#color(white)(xx)3y=2x-10#
#=>3y=2xxcolor(red)(11/2)-10#
#=>3y=1#

#=>color(red)(1/3xx)3y=color(red)(1/3xx)1#
#=>y=1/3#