How do you solve the system of equations #8x+7y=-51# and #x-y=3#?

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Answer 1 · 2016-10-31T10:43:07

#x = -2#
#y = -5#

Scale either equation (or both) such that the coefficient of one of the variables will have the same absolute value for both equations

#[1] 8x + 7y = -51#
#[2] x - y = 3#

Multiply #[2]# by #7#

#[3] => 7(x - y = 3)#

#[3] => 7x - 7y = 21#

Note that the absolute value of #y#'s coefficient is #7# for both #[1]# and #[3]#. If we add #[1]# and #[3]#, we have

#[1] 8x +7y = -51#
#[3] 7x - 7y = 21#

#[4] => 15x + 0y = -30#

#=> x = -2#

Now that we know the value of #x#, use it in either #[1]#, #[2]#, or #[3]# to get #y#. Let's use #[2]#

#[2] x - y = 3#
#=> -2 - y = 3#
#=> y = -5#