How do you solve the system 5x – 3y = 13 and 4x – 3y = 11?

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Answer 1 · 2018-05-21T13:14:32

#x=2# and #y=-1#

After subtracting second equation from first one,

#(5x-3y)-(4x-3y)=13-11#

#x=2#

Hence,

#5*2-3y=13#

#10-3y=13#

#-3y=3#, thus #y=3/(-3)=-1#

Answer 2 · 2018-05-21T13:17:25

#(2, -1)#

Solving by Elimination

Multiply the first equation by #-1# to temporarily eliminate #y#. Then add to the second equation (unmodified).

#-(5x - 3y = 13)#
#-5x + 3y = -13#
#4x - 3y = 11#

#-x = -2#
#x = 2#

Substitute into either equations to solve for #y#
#5(2) - 3y = 13#
#10 - 3y = 13#
# - 3y = 3 #
#y = -1#

Answer: #(2, -1)#