Solve both equations for #-2x# and set them equal to each other.
#−2x−y=11#
so #-2x = 11 + y#
#−2x−9y=3#
so #-2x = 3 + 9y#
Because both of the equations are equal to #-2x,# they are equal ro each other.
#11 + y = - 2x# and #-2x= 3 + 9y#
#11 + y = 3 + 9y#
1) Subtract #y# from both sides to get all the #y#'s together
#11 = 3 + 8y#
2) Subtract 3 from both sides to isolate the #8y# term
#8 = 8y#
3) Divide both sides by 8 to isolate #y#
#1 = y# #larr# answer for #y#
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To find #x#, sub in #1# for #y# and solve for #x#
#−2x−y=11#
#- 2x - 1 = 11#
1) Add 1 to both sides to isolate the #- 2x# term
#- 2x = 12#
2) Divide both sides by #- 2# to isolate #x#
#x = - 6# #larr# answer for x
Answer:
#x = - 6#
#y = 1#
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Check
Sub in the values for #x# and #y# back into the original equations.
(1) #−2x−9y=3#
#(-2)(-6) - (9)(1)# is supposed to equal #3#
#12 -9# is supposed to equal #3#
#3# does equal #3# ✓
..................................
(2) #−2x−y=11#
#(-2)(-6) - 1# is supposed to equal #11#
#12 - 1# is supposed to equal #11#
#11# does equal #11# ✓
