How do you solve the following system?: # 2x + 3y = 1 , -3x + 7y = 1 #

2 Answers
Binayaka C.
May 19, 2018

Solution: # x = 4/23 , y =5/23 #

Explanation:

# 2 x + 3 y =1 ; (1) , -3 x +7 y =1 ; (2)# Multiplying equation

(1) by #3# and equation (2) by #2# we get,

# 6 x + 9 y =3 ; (3) , -6 x +14 y =2 ; (4)# Adding equation

(3) and equation (4) we get, # 23 y= 5 :. y =5/23#. Putting

# y =5/23# in equation (1) we get, #2 x +3*5/23=1# or

#2 x=1-15/23 or 2 x = (23-15)/23 or 2 x =8/23 or x = 4/23#

Solution: # x = 4/23 , y =5/23 #[Ans]

Bill Jorgensen
May 19, 2018

#y=5/23#

#x=4/23#

Explanation:

#2x+3y=1#
#-3x+7y=1#

Probably the easiest way to solve this is by elimination; notice there is a GCD of #2x# and #-3x# of #6x# so let's multiply both equations by 3 and 2 respectively:

#3(2x+3y=1)#
#2(-3x+7y=1)#

#6x+9y=3#
#-6x+14y=2#

now add the equations together, notice the x terms are eliminated:

#23y=5#

#y=5/23#

now use either original equations with the y value you found to solve for x:

#2x+3(5/23)=1#

#x=4/23#

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