How do solve the following linear system?: # -4x-15y=-1 , -3x+7y=-1 #?

1 Answer
Jul 31, 2016

Answer:

The same values of #x# and #y# must satisfy both equations

Explanation:

Probably the easiest way to solve this is to manipulate the equations to bring them to a more convenient form in which both have the same coefficient for #x#. Multiply the fist one by #3# and the second one by #4#:

#-12x-45y=-3#
#-12x+28y=-4#

This system is equivalent to the given one. Now we subtract the second form the first, and we get:
#-73y=1#, and then #y=-1/73#. Now replacing the #y# value in either equation, say the first one, we have:

#-12x-45*1/73=-3#, so

#-12x=-3+45/73# so

#-12x=(-219+45)/73#, and then

#-12x=-174/73#, and this results in

#x=(-1/12) * (-174/73)#, and simplifying

#x=29/146#