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

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Answer 1 · 2018-04-03T07:51:59

#x = -7, y=16/3#

You may solve the system via substitution:

#2x+3y=2#
#x+3y=9#

From the second equation you can exctract #x=9-3y#

Substituting back in the first equation, you have

#2x+3y=2#
#\iff#
#2(9-3y)+3y=2#
#\iff#
#18-6y+3y=2#
#\iff#
#18-3y=2#
#\iff#
#16=3y#

And thus #y = 16/3#

Once #y# is known, we can substitute it again into

#x=9-3y = 9-3*16/3 = 9-16 = -7#