How do solve the following linear system?: # 3x-8y=6, 2x - 5y=3 #?

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Answer 1 · 2017-06-23T11:35:14

By some arrangement, #x=-6# and #y=-3#

Expand the first original equation with #2# and the second original equation with #-3# to get only equation having one unknown:

#6x - 16y = 12#
#-6x + 15 y = -9

Add the terms (of the above equations, yielding
#-16 y + 15 y = 12-9#

# -y=3#

or #y=-3#

Now put this value in any equation (for example the first equation):

#3x - (8times-3) = 6#

#3x + 24 = 6#

#3x = 6-24#

#3x = -18#

#x = -6#

This is your answer: #x=-6# and #y=-3#