How do solve the following linear system?: # -x-7y=14 , x-2y=8 #?

1 Answer
Apr 2, 2016

Answer:

#(x,y)=(28/9,-22/9)#

Explanation:

Solve by elimination and substitution

#color(blue)(-x-7y=14#

#color(blue)(x-2y=8#

We can eliminate #x# in the first equation by #-x# in the second equation

Add both the equations

#rarr(-x-7y=14)+(x-2y=8)#

#rarr-9y=22#

#color(green)(rArry=-22/9#

Substitute the value of #y# to the second equation

#rarrx-2(-22/9)=8#

#rarrx+44/9=8#

#color(green)(rArrx=8-44/9=28/9#

#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~#

Check (#-x-7y=14#)

#rarr-28/9-7(-22/9)=14#

#rarr-28/9+154/9=14#

#rarr(-28+154)/9=14#

#rarr126/9=14#

#color(orange)(rArr14=14#

#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~#

Check (#x-2y=8#)

#rarr28/9-2(-22/9)=8#

#rarr28/9+44/9=8#

#rarr(28+44)/9=8#

#rarr72/9=8#

#color(violet)(rArr8=8#

#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~#

#:. color(blue)( ul bar |(x,y)=28/9,-22/9|#