How do you solve this system of equations: # x +2y = 3 and 3x +5y=15 #?

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Answer 1 · 2017-09-30T15:40:40

#y=-6#
#x=15#

We will start by multiplying the first equation by 3 on both sides.

#3(x+2y)=3(3)#
#3x+6y=9#

Now that we have #3x# in both equations we can subtract the equations form each other to eliminate the #x#'s.

#color(red)(3x+6y=9)#
#-#
#color(blue)(3x+5y=15)#

#color(red)(3x)color(blue)(-3x)color(red)(+6y)color(blue)(-5y)=color(red)9color(blue)(-15)#
#y=-6#

We can substitute this back into the one of the original equations to find #x#.

#x+2(-6)=3#
#x-12=3#
#x=15#