How do you solve the following system?: # x - y = -6, 2x -5y=7 #

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Answer 1 · 2016-03-13T13:29:27

The solution for the system of equations is:
#color(green)(x=-37/3#

#color(green)(y= (-19)/3#

#x-y=-6#, multiplying this equation by #2#
#color(blue)(2x)-2y=-12#...............equation #(1)#

#color(blue)(2x) - 5y =7#........................equation #(2)#

Solving by elimination.

Subtracting equation #2# from #1# results in elimination of #color(blue)(2x)# from the equations.

#cancelcolor(blue)(2x)-2y=-12#
#-cancelcolor(blue)(2x) + 5y =-7#

#3y = -19#

#color(green)(y= (-19)/3#

Finding the value of #x# from equation #1#:

#x-y=-6#

#x=-6 + y#

#x=-6 + color(green)(((-19)/3))#

#x=-18/3 + ( (-19)/3)#

#color(green)(x=-37/3#