How do you solve the following system: #3x - 4y = -10, 4x + 7y = 6x#?

1 Answer
Feb 8, 2016

Answer:

#x=-70/13" "#I have left the derivation of y for the reader to determine.

Explanation:

Given:

#3x-4y=-10" "#.................................(1)
#4x+7y=6x" "#......................................(2)
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Consider equation (2)

Subtract #4x# from both sides

#7y=2x#

Divide both sides by 7

#y=2/7x" "......................................(2_a)#

Substitute #(2_a)" into "(1)#

#3x-4(2/7x)=-10" "...................(1_a)#

#3x-8/7x=-10#

#x(21-8)/7=-10#

#x=-(7/13xx10)#

#x=-70/13" ".......................................(1_b)#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

You can now find #y# by substituting #(1_b)# into either of (1) or (2).

I will leave that for the reader to do