How do you solve the following system?: #8x +y =3 , 4x +12y = -4#

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Answer 1 · 2015-11-11T07:27:16

The solution for the system of equations is:
#color(blue)(x=10/23, y=-11/23#

#color(blue)(8x)+y=3#....equation #1#

#4x+12y=−4#, multiplying this equation by #2#
#color(blue)(8x)+24y=−8#......equation #2#

Now, we solve by elimination :
Subtracting equation #2# from #1#

#cancelcolor(blue)(8x)+y=3#
#-cancelcolor(blue)(8x)-24y=+8#

#-23y=11#

#y=11/-23#

#y=color(blue)(-11/23#

Now we substitute #y# in any of the equations to find #x#

#8x+y=3#

#8x -11/23=3#

#8x =3+ 11/23#

#8x =80/23#

#x =cancel80/(23*cancel8)#

#color(blue)(x =10/23#