How do you solve the system of equations #2x + 3y = 13# and #3x - 5y = - 9#?

1 Answer
jk.13
Apr 4, 2018

#(x,y)=(2,3)

Explanation:

#2x=13-3y#
#x=13/2-3/2y# solve for #x# in terms of #y# in the first equation
#3(13/2-3/2y)-5y=-9# plug into the other equation
#39/2-9/2y-10/2y=-18/2# distribute and set a common denominator
#39/2-19/2y=-18/2#
#39-19y=-18# this is a matter of personal preference, but I like to multiply the whole equation by the denominator to get rid of fractions (for now)
#-19y=-57#
#y=57/19#
#y=3#

Now, going back to the other equation
#2x+3(57/19)=13# plug in value of y
#2x+171/19=13#
#2x+9=13#
#2x=4#
#x=2#

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