How do you solve the following system?: #3x -9y =-13 , -2x +17y = 8#

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Answer 1 · 2016-04-29T22:47:47

#x=-139/69#
# y = 50/69#

# 3x-9y = -13# and
#-2x+17y = 8#

multiply first statement by "2" and the second statement by "3" to get to a common coefficient of 'x'
#2(3x-9y) = 2(-13)#
#3(2x+17y) = 3(8)#

#6x-18y = -26#
#6x+51y = 24#

then, subtract second statement from first statement
#-69y = -50#

now that y is isolated, we know that
# y = 50/69#

to solve for x, substitute the value for 'y' into one of the statements

#3x-9(50/69) = -13#

divide the statement by 3
#x-3(50/69)=-13/3#
#x-(50/23)=-13/3#
#x=-13/3 +50/23#

lastly, solve for lowest common denominator
#x=(-299 + 150)/69=-139/69#