How do you solve the system # x - 3y = 3# and #2x + 9y = 11# by substitution?

1 Answer
Alan P.
May 29, 2015

#[1]color(white)("XXXXX")x-3y = 3#
#[2]color(white)("XXXXX")2x+9y = 11#

Rearrange [1] to get an expression for #x#
#[3]color(white)("XXXXX")x=3+3y#

Substitute the expression for #x# from [3] into [2]
#[4]color(white)("XXXXX")2(3+3y)+9y = 11#

Simplify
#[5]color(white)("XXXXX")6+6y+9y = 11#
#[6]color(white)("XXXXX")15y= 5#
#[7]color(white)("XXXXX")y=1/3#

Substitute the value of #y# from [7] into [1]
#[8]color(white)("XXXXX")x-3(1/3) = 3#

Simplify
#[9]color(white)("XXXXX")x=4#

The solution is #(x,y) = (4,1/3)#

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