How do you solve system of equations #y = x+1# and #y = 2x -1#?

2 Answers
bp
Mar 29, 2015

x=2; y=3

Substitute y= x+1 from the first equation into the second equation. it would become x+1= 2x-1. Now add 1 on both sides and also subtract x from both sides. It would become 2=x. that is x=2. Now in the 1st equation, plugin x=2, to get y= 2+1 =3.

Antoine
Mar 29, 2015

#y = x + 1# ...equation 1
#y = 2x - 1# ...equation 2

subtract equation 1 from equation 2.

equation 2 - equation 1
#=> y - y = [2x - 1] - [x + 1]#

#=> 0 = 2x - x - 1 -1#

#=> 0 = x - 2#
# x - 2 = 0# Right ?!

#=> x = 2#

put #x = 2# in equation 1 OR 2

in equation 1:
# y = x + 1#
#=> y = 2 + 1#
# => y = 3#

OR
in equation 2:
#y = 2x - 1#
#=> y = 2*(2) - 1#
# y = 4 - 1#
#=> y = 3# As above for equation 1

Hence #x = 2# and #y = 3#

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