How do you solve the following system of equations?: #3x-y=7 , 4x+3y=8#?

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Answer 1 · 2015-12-27T14:29:29

The solution for the system of equations is

#color(blue)(x=29/13, y=-4/13#

#3x-y=7#, multiplying the equation by #3#
#9x-color(blue)(3y)=21#.....equation #(1)#

#4x+color(blue)(3y)=8#........equation #(2)#

Solving by elimination

Adding equations #1# and #2#:

#9x-cancelcolor(blue)(3y)=21#

#4x+cancelcolor(blue)(3y)=8#

#13x=29#

#color(blue)(x=29/13#

Now, we find #y# by substituting #x# in equation #1#:

#3x-y=7#

#3x-7=y#

#3 xx color(blue)(29/13)-7=y#

#87/13-7=y#

#87/13-91/13=y#

#color(blue)(y=-4/13#