How do you solve the following system?: #-1/2x+5y=-20 , -x+6y=7 #

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Answer 1 · 2015-11-28T04:07:40

Answer: #(-155/2 , -47/2)#

Equation 1: #-1/2 x + 5y = -20#

Equation 2: #-x + 6y = 7#

Multiply equation 1 by #-2# to eliminate fraction
#-2[-1/2x +5y =-20}] hArr# #color(red)(x -10y = 40)#

Take equation 2, solve for #x#

#-x+6y = 7 hArr color(red)(6y-7=x)#

Substitute #color(red)(6y-7=x)# into first equation

#color(red)(6y-7)-10y = 40#

#-4y= 47#

#color(blue)(y= -47/4)#

Substitute
#6(-47/4)-7= x#

#-141/2 -14/2 = x#

#color(blue)(-155/2 = x)#