How do solve the following linear system?: #-9x + 5y = 16 , x - 3y = -6 #?

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Answer 1 · 2016-05-10T08:19:02

The solution for the system of equations is:
#color(blue)(x = (- 9 )/ 11 #

#color(blue)(y = 19 / 11#

# color(green)(- 9x) + 5y = 16#..............equation #(1)#

#x - 3y = - 6# , multiplying by #9#
#color(green)(9x) - 27y = - 54#............equation #(2)#

Solving by elimination:

Adding equations #1# and #2:#

# cancelcolor(green)(- 9x) + 5y = 16#
#cancelcolor(green)(9x) - 27y = - 54#

#-22y = -38#

# y = (-38) / (-22)#

#color(blue)(y = 19 / 11#

Finding #x# from equation #2:#

#x - 3y = - 6#

#x = - 6 + 3y #

#x = - 6 + 3 * (19 / 11) #

#x = - 6 + 57 / 11 #

#x = (- 66 + 57 )/ 11 #

#color(blue)(x = (- 9 )/ 11 #