How do you solve the system of equations #2x+3y=13# and #x=2y-4#?

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Answer 1 · 2016-04-08T07:49:34

The solution for the system of equations is:
#color(green)(x=2#

#color(green)(y=3#

#color(blue)(2x) + 3y = 13#......................equation #(1)#

#x= 2y - 4#, multiplying by #2#

#2x= 4y - 8#

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

Solving by elimination:

Subtracting equation #2# from #1#:
#cancelcolor(blue)(2x) + 3y = 13#

#-cancelcolor(blue)(2x) + 4y = + 8#

#7y = 21#

#y = 21/7#

#color(green)(y=3#

Finding the value of #x# from equation #2#:
#x= 2y - 4#

#x= 2 * color(green)(3) - 4#

#x= 6 - 4 = 2#

#color(green)(x=2#