How do solve the following linear system?: # -3x+7y=-1 , -x+3y=-5 #?

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Answer 1 · 2015-12-04T16:10:58

The solution for the system of equations is
#color(blue)(x=-16,y=-7#

#-3x+7y=-1#......equation #1#

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

Solving by substitution :

Substituting equation #2# in equation #1#:

#-3x+7y=-1#

#-3 * (color(blue)(3y+5))+7y=-1#

#(-3) * (3y) + (-3) * (5)+7y=-1#

#-9y -15+7y=-1#

#-9y +7y=-1 +15#

#-2y=14#

#y=-14/2#

#color(blue)(y=-7#

Finding #x# by substituting #y# in equation #2#

#color(blue)(x=3y+5#

#x=3 * (-7)+5#

#x=-21+5#

#color(blue)(x=-16#

The solution for the system of equations is
#color(blue)(x=-16,y=-7#