How do you solve the following system?: #9y = -3x - 9 , y=-x + 12 #

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Answer 1 · 2016-02-01T16:35:08

#color(blue)(y=-27)#
#color(blue)(x= 39)#

Given:

#9y=-3x-9#..........................(1)
#y=-x+12#............................(2)

Two equations; two unknowns thus solvable

#color(blue)("Method:")#

#color(brown)("Eliminate one of the unknowns by substitution, so that we are ")##color(brown)("solving for 1 unknown in 1 equation.")#

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("To find the value of "x)#

Substitute equation (2) into equation (1) giving:

#9(-x+12)=-3x-9" "......................(2_a)#

#-9x+108=-3x-9#

Collecting like terms we have

#9x-3x=108+9#

#3x=117#

Divide both sides by 3 giving:

#color(blue)(x= 39)#........................................(3)

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("To find the value of "y)#

Substitute equation (3) into equation (2) (the easier of the two!)

#y=-(39)+12 = -27#

#color(blue)(y=-27)#