How do you solve the following system: #3x - 2y = 9, 6x + y = 2#?

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Answer 1 · 2016-04-08T07:42:10

The solution for the system of equations is:
#color(green)(x = 13/15#

#color(green)(y = (-16)/ 5#

#3x - 2y = 9#, multiplying by #2#
#color(green)(6x) - 4y = 18#.............equation #(1)#

#color(green)(6x) + y =2 #.................equation #(2)#

Solving by elimination.

Subtracting equation #2# from #1#:

#cancelcolor(green)(6x) - 4y = 18#
#-cancelcolor(green)(6x) - y =-2 #

#-5y = 16#

#color(green)(y = (-16)/ 5#

Finding #x# from equation #1#

#3x - 2y = 9#

#3x = 9 + 2y#

#3x = 9 + 2 * (-16/5)#

#3x = 9 -32/5#

#3x = 45/5 -32/5#

#3x = 13/5#

#x = 13/(5 * 3)#

#color(green)(x = 13/15#