How do you solve the following system: # 8x-7y=-39, 7x − 5y = −11 #?

2 Answers
Nov 5, 2017

Answer:

#x=118/9, y=185/9#

Explanation:

#8x-7y=-39#...(1)
#7x-5y=-11#...(2)

(1)*5:
#40x-35y=-195#...(3)

(2)*7:
#49x-35y=-77#...(4)

(4)-(3):
#9x=118#
#x=118/9#

Sub x=118/9 into (1)
#944/9-7y=-39#
#-7y=-1295/9#
#y=185/9#

Nov 5, 2017

Answer:

I have solved #1/2# of it left the remainder for you to do.
Check your solution with that in the graph.

Explanation:

#color(blue)("Preamble")#

I choose to answer this the traditional way.

Example of the principle used. When I realised this (long time ago) it opened the door for me to a whole new way of thinking.

Suppose we have #color(white)("d")color(green)(3x-6=5)#

Then it is also true that

#color(green)(color(white)("dddddddddd") color(red)(2xx)(3x-6)=color(red)(2xx)(5))#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Answering the question")#

Given:
#8x-7y=-39" "....................Equation(1)#
#7x-5y=-11" "......................Equation(2)#

If we change one or both of these then subtract it will eliminate one of the unknown. Then we have 1 equation with 1 unknown and thus solvable

Lets 'get rid' of the #y's#

Multiply #Eqn(1)# by 5 and #Eqn(2)# by 7

#color(white)("d")40x-35y=-195" ".........Equation(1_a)#
#color(white)("d")ul(49x-35y=-77" "............Equation(2_a)larr" Subtract")#
#-9x+color(white)("d")0y= -118#

Divide both side by -9

#x=+118/9#

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
I will let you determine #y#. Just substitute this value into one of the equation.
Tony B