How do you solve this system of equations: # y = -5/3 x +3 and y = 1/3x -3#?

1 Answer
Nallasivam V
Apr 3, 2017

#x=3#
#y=-2#

Explanation:

Given -

#y=-5/3x+3# ----------------- (1)
#y=1/3x-3# -------------------(2)

METHOD - I

#y=-5/3x+3# ----------------- (1) #xx 3#
#y=1/3x-3# -------------------(2)#xx3#

#3y=-5x+9# ------------------(3)
#3y=x-9# -----------------------(4) ----- #(3) - (4)#

#0=-6x+18#
#-6x+18=0#
#-6x=-18#
#x=(-18)/(-6)=3#

#x=3#

Substitute #x=3# in equation (4)

#3y=x-9#
#3y=3-9=-6#

#y=(-6)/3=-2#

#-2#

METHOD - II

Substitute #y=1/3x-3# in the first equation. We get -

#1/3x-3=-5/3x+3#

#1/3x=-5/3x+3+3#
#x/3+(5x)/3=3+3#
#(x+5x)/3=6#
#(6x)/3=6#
#2x=6#
#x=6/2=3#

#x=3#

Substitute #x=3# in the equation (2)

#y=1/3x-3#
#y=1/3(3)-3#
#y=1-3#
#y=-2#

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