How do you solve the following system?: #-8x -5y =13, -7x +y = -2#

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Answer 1 · 2015-12-26T08:31:55

The solution for the system of equations is

#color(blue)(x=-3/43,y=-107/43#

#-8x-color(blue)(5y)=13#..........equation #(1)#

#-7x+y=-2#, multiplyting by #5#

#-35x+color(blue)(5y)=-10#..equation #(2)#

Solving by elimination.

Adding equations #1# and #2#

#-8x-cancelcolor(blue)(5y)=13#

#-35x+cancelcolor(blue)(5y)=-10#

#-43x=3#

#color(blue)(x=-3/43#

Finding #y# by substituting #x# in equation #2#:
#-7x+y=-2#

#-7 xxcolor(blue)((-3/43))+y=-2#

#21/43+y=-2#

#y=-2- 21/43#

#y=-86/43- 21/43#

#color(blue)(y=-107/43#