How do you solve the system #-2x+3y=-9# and #-x+-3y=-3#?

1 Answer
Jun 24, 2015

Answer:

Solve the two possibilities separately:
#{(-2x+3y=-9),(-x+3y=-3):} and {(-2x+3y=-9),(-x-3y=-3):}#
giving #(x,y)=(6,1)# and #(x,y)=(4,-1/3)#

Explanation:

Case 1:
#{([1]color(white)("XXX")-2x+3y=-9),([2]color(white)("XXX")-x+3y=-3):}#
subtracting [2] from [1]
#[3]color(white)("XXXX")##-x =-6#
#[4]color(white)("XXXX")##x=6#
substituting #x=6# in [2]
#[5]color(white)("XXXX")##-6+3y = -3#
#[6]color(white)("XXXX")##y=1#

Case 2:
#{([7]color(white)("XXX")-2x+3y=-9), ([8]color(white)("XXX")-x-3y=-3):}#

#[9]color(white)("XXXX")-3x = -12#
#[10]color(white)("XXXX")x==4#

#[11]color(white)("XXXX")-4-3y = -3#
#[12]color(white)("XXXX")y=-1/3#