How do you solve the following system: #3x - 4y = -23, 6x + 7y = -9 #?

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Answer 1 · 2016-05-07T03:13:42

#(-3/2, 37/8)#

#[1] 3x - 4y = -23#
#[2] 6x + 7y = -9#

Get the equivalent of either variable from either equation.
For example, get the equivalent of #x# from #[1]#

#3x - 4y = -23#
#=> 3x = 4y -23#
#=> x = (4y - 23)/3#

Substitute the obtained equivalent of the desired variable into the other equation.

#6x + 7y = -9#

#=> 6((4y - 23)/3) + 7y = -9#

#=> 2(4y - 23) = -9#

#=> 8y - 46 = -9#

#=> 8y = 37#

#=> y = 37/8#

Solve for the other variable now that we know the value of one variable

#3x - 4y = -23#

#=> 3x - 4(37/8) = -23#

#=> 3x - 37/2 = -23#

#=> 6x - 37 = -46#

#=> 6x = -9#

#=> x = -9/6 = -3/2#