How do you solve the following system: #6x + y = 2, 3x - 4y = -10#?

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Answer 1 · 2016-03-15T11:06:35

#x = -2/27# and #y = 22/9#

#6x+y = 2# ---------Eqn #1#
#3x-4y=-10# ---------Eqn #2#

Multiplying Eqn #2# by #2#

#6x-8y=-20# ---------Eqn #3#

Subtracting Eqn #1# from Eqn #3#
Note: Subtracting changes the bottom equation's sign

#cancel(6x)+y = 2#
#cancel(-6x)+8y=20#

#9y = 22 implies y = 22/9#

put #y = 22/9# in Eqn #2#

#3x-4(22/9)=-10#

#3x-88/9=-10#

#27x-88=-90#

#27x=-90+88#

#27x = -2 implies x = -2/27#