What is the solution to the following system of linear equations: #4x-y=-6# #x-2y=-5#?

1 Answer
Sep 11, 2015

Answer:

#{(x=-1), (y=2) :}#

Explanation:

Your starting system of equations looks like this

#{(4x-y = -6), (x-2y = -5) :}#

Multiply the first equation by #(-2)# to get

#{(4x-y = -6 | * (-2)), (x-2y = -5) :}#

#{(-8x+2y = 12), (" "x-2y = -5) :}#

Notice that if you add the two equations by adding the left-hand sides and the right-hand sides separately, you can eliminate the #y#-term.

The resulting equation will have only one unknown, #x#.

#{(-8x+2y = 12), (" "x-2y = -5) :}#
#stackrel("-------------------------------------------")#

#-8x + color(red)(cancel(color(black)(2y))) + x - color(red)(cancel(color(black)(2y))) = 12 + (-5)#

#-7x = 7 implies x = 7/((-7)) = color(green)(-1)#

Plug this value of #x# into one of the two original equations to get the value of #y#

#4 * (-1) - y = -6#

#-4 - y = -6#

#-y = -2 implies y = ((-2))/((-1)) = color(green)(2)#

The solution set for this system of equations will thus be

#{(x=-1), (y=2) :}#