How do solve the following linear system?: #-4x + 4 = -y, 3x + 6y + 13 = 0 #?

1 Answer
EZ as pi
May 31, 2017

#x = 11/27 and y = -2 17/27#

Explanation:

It might be better to work on the first equation a little and multiply by #-1# so the #y# term is positive. Then we have an equation which is suitable for the substitution method:

#-4x +4 = -y" "rarr (xx-1)" "rarrcolor(blue)(4x-4 = y)#

Substitute #color(blue)((4x-4))# for #y# in the other equation:

#3x+6color(blue)( y) +13=0#

#3x+6color(blue)((4x-4)) +13=0" "larr# only #x# terms

#3x+24x = -13+24#

#27x = 11#

#x = 11/27#

Now use #x=11/27# to find a value for #y#

#y =4x-4 = 4(11/27)-4#

#y= -2 10/27#

Checking into the second equation confirms these results:
#0=0#

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