How do you solve the following linear system #-x + 2y = 6 , x - 4y = -3 #?

1 Answer
Dec 14, 2015

Answer:

#color(white)(xx)x=-9color(white)(x) "and" color(white)(x)y=-3/2#

Explanation:

#color(white)(xx)-x+2y=6, x-4y=-3#

With a different approach:
#color(white)(xx)-x+2y=6<=>color(red)(y=(x+6)/2)#
and
#color(white)(xx)x-4y=-3<=>color(red)(y=(x+3)/4)#

#color(white)(xx)(x+6)/2=y#
#=>(x+6)/2=color(blue)((x+3)/4)#

Multiply both side by #color(green)4# to simplify right side:
#color(white)(xx)color(green)(4xx)(x+6)/2=color(green)(4xx)(x+3)/4#
#=>color(red)2x+color(red)12=x+3#

Finally add #color(red)(-x-12)# to both side to find #x#.
#=>2x+12color(red)(-x-12)=x+3color(red)(-x-12)#
#=>x=-9#

#color(white)(xx)y=(x+6)/2#
#color(white)(xxx)=(color(blue)(-9)+6)/2#
#color(white)(xxx)=-3/2#