How do you solve the system of equations #y= - x + 11# and #2x + 3y = 26#?

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Answer 1 · 2018-01-31T22:12:49

#x = 8#
#y = 3#

#y = -x + 11#
#2x+3y = 26#

If we know #y = -x + 11# then we can sub #y# for the other equation. This gives us:

#2x+3color(red)y = 26#

#2x+3(color(red)(-x+11)) = 26#

From here we solve for #x#:

#2x-3x+33=26#

#2x-3x = 26 -33#

#-1x = -8#

#color(blue)(x=8)#

Now we know #x# we can solve for #y# using our first equation:

#y = -color(red)x + 11#
#y = -color(red)8 + 11#
#color(blue)(y = 3)#