How do you solve the following system of equations?: #-x – 2y = 12 , 12x+y=8#?

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Answer 1 · 2015-12-13T19:19:39

(28/23 , -152/28)#

#{(-x-2y=12),(12x+y=8):}#

Multiply the first equation by 2, to eliminate #y#

#{(-x-2y=12),(color(red)2*(12x+y=8)):}#

#=> {(-x-2y= 12), (24 x + 2y = 16):}#

#=> {(-x cancel(-2y)= 12), (24 x cancel(+ 2y) = 16):}#

#=> 23x =28#

#=> (13x)/23= 28/23 => x= 28/23#

Substitute #x= 28/23# into one of the original equation to solve for #y#

We will use this one #12x + y = 8#

#12(28/23) + y = 8#

#336/23 + y = 184/23#

#y = 184/23 - 336/23#

#y = -152/23#

Answer :#(28/23 , -152/28)#