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

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Answer 1 · 2016-03-03T18:25:56

The solution for the system of equations is:
#color(blue)(x=1#
#color(blue)(y=1#

#2x +y=3#, multiplying by #2#
#4x +color(blue)(2y)=6#.......equation #(1)#

#5x-color(blue)(2y)=3#........equation #(2)#

Solving by elimination

Adding equations #(2)# and #(1 )# results in elimination of #color(blue)(2y#

#4x +cancelcolor(blue)(2y)=6#

#5x-cancelcolor(blue)(2y)=3#

#9x=9#

#x=9/9#

#color(blue)(x=1#

Finding #y# from equation #1#:
#2x +y=3#

# y=3 - 2x#

# y=3 - 2 xx 1#

# y=3 - 2#

#color(blue)(y=1#