How do you solve the following system: #7x-2y= -67, x+3y=3 #?

1 Answer
Feb 5, 2016

Answer:

#x=10 5/19" "# I will let the reader solve for #y#. Approach given.

Explanation:

Given:
#7x-2y=-67#.................................(1)
#x+3y=3#............................................(2)
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Rewrite equation (2) to give:

#y=-1/3x+1" ".......................(2_a)#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Substitute #(2_a)# into (1) giving:

#7x-2(-1/3x+1)=-67" "....(1_a)#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Solving for "x)#

#7x+2/3x-2=-67#

#19/3 x=-65#

#color(blue)(x=-195/19" "->10 5/19)#

#color(purple)("Notice how I keep fractional values instead of decimals.")##color(purple)("It is more precise that way!")#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

I will let you solve for #y#. Just substitute the value for #x" in "(2_a)#
#(2_a)# looks as though it is the simplest one to use!