How do you solve the system of equations #-2x+6y = 6# and #-7x+8y=-5#?

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Answer 1 · 2018-04-18T18:48:33

#=>x = 3, y = 2#

I would suggest substitution. Dividing the first equation by #-2# allows for #x# to be isolated.

#[1]" " -2x+6y=6#
#[2]" " -7x+8y=-5#

Dividing #[1]# by #-2#.

#x -3y = -3#

#[3]" " x = 3y-3#

We can now substitute #[3]# into #[2]#.

#-7(3y-3) + 8y = -5#

#-21y + 21 + 8y = -5#

#-13y + 21 = -5#

#-13y = -26#

#[4]" " y = 2#

We now substitute #[4]# into #[1]#.

#-2x + 6(2)= 6#

#-2x + 12 = 6 #

#-2x = -6#

#[5] " " x = 3#

From #[4]# and #[5]#, our solution is

#=>x = 3, y = 2#