How do you solve the following system?: # 2x - y = 5 , x + 2y = 3 #

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Answer 1 · 2016-01-05T17:38:59

The solution for the system of equations is

#color(blue)(x=13/5, y=1/5#

#color(blue)(2x)-y=5#....equation #(1)#

#x +2y=3#, multiplying by #2#

#color(blue)(2x) +4y=6#....equation #(2)#

Solving by elimination

Subtracting equation #2 # from #1#:

#cancelcolor(blue)(2x)-y=5#
#-cancelcolor(blue)(2x) -4y=-6#

#-5y=-1#

#y=(-1)/(-5)#

#color(blue)(y=1/5#

Finding #x# from equation #2#

#x +2y=3#

#x =3-2y#

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

#x =3-2/5#

#x =15/5-2/5#

#color(blue)(x =13/5#