How do solve the following linear system?: # x+2y=1 , x+y=6 #?

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Answer 1 · 2015-11-28T04:51:59

#(11, -5)#

Equation 1: #x+2y= 1#
Equation 2 : #x+y= 6#

To solve by substitution method, take equation 1, solve for #x#
#x+2y= 1# #hArr color(red)( x= 1-2y)#

Then substitute #color(red)(x= 1-2y)# into equation 2

#=> color(red)((1-2y)) + y = 6#

#=>1-y= 6#
#=> -y= 5# #=> color(blue)(y = -5)#

Substitute the solution for #y# into either equation 1 equation 2

#=> x+2color(blue)*((-5))= 1#
#=> x-10 = 1# #=>color(blue)( x= 11)#

We can verify the solution by substitute the solution into the original equations

Eq 1: #(11)+ 2(-5) = 1#
#=> 1= 1#

Eq 2: #11+(-5) = 6#
#=> 6= 6#