How do solve the following linear system?: # x+y=-4, 3x – 4y = 7 #?

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Answer 1 · 2015-12-06T12:57:46

The solution for the system of equations is
#color(blue)(x=-9/7 , y=-19/7#

#color(blue)(3x)-4y = 7#.........equation #(1)#

#x+y=-4#, multiplying this equation by #3#
#color(blue)(3x) +3y = -12#....equation #(2)#

Solving by elimination

Subtracting equation #2# from #1# results in elimination of #color(blue)(3x#

#cancelcolor(blue)(3x)-4y = 7#
#-cancelcolor(blue)(3x) -3y = +12#

#-7y=19#

#y=19/(-7)#

#color(blue)(y=-19/(7)#

Finding #x# by substituting #y# in equation #2#:
#x+y=-4#

#x=-4-y#

#x=-4-(-19/7)#

#x=-4+19/7#

#x=-28/7+19/7#

#color(blue)(x=-9/7#