How do you solve the following linear system: # 2x-5y=-4, x + 6y = 4, #?

1 Answer
Apr 3, 2018

Answer:

#x=-4/17#

#y=color(white)("dd")12/17#

Explanation:

This is one of two approaches:

Given:
#2x-5y=-4" "..........Equation(1)#
# color(white)("d") x+6y=+4" "..........Equation(2)#

Multiply both sides of #Eqn(2)# by 2

#2x-color(white)("d")5y=-4" ".........Equation(1)#
#ul(2x+12y=+8" ".........Equation(2_a)larr" Subtract" )#
#color(white)("d")0-17y=-12#

By choosing negative it will change the #y# term into positive.
Divide both sides by #(-17)#

#color(blue)(color(white)("ddddddddddd")ul(bar(| color(white)(..) y=12/17color(white)(..)|)))#

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Substitute for #color(red)(y=12/17)# into #Eqn(2)#

#color(green)(x+6color(red)(y)=4 color(white)("dddd")->color(white)("dddd")x+(6color(red)(xx12/17))=4 )#

#color(white)("ddddddddddddd")->color(white)("dddd")x+color(white)("ddd")72/17color(white)("d.d")=4#

#color(blue)(color(white)("ddddddddddd")ul(bar(| color(white)(..) x=-4/17color(white)(..)|)))#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Check")#

#2x-5y=-4" "..........Equation(1)#
#color(white)("d")x+6y=+4" "..........Equation(2)#

#2(-4/17)-5(12/17)=-4" "..........Equation(1)#
#color(white)("d")(-4/17)+6(12/17)=+4" "..........Equation(2)#

#-8/17-60/17=-4" "..........Equation(1)#
#-4/17+72/17=+4" "..........Equation(2)#

#-4=-4" "..........Equation(1)#
#+4=+4" "..........Equation(2)#