How do you solve the system of equations #-16x - 4y = 12# and #- 4x + y = - 11#?

1 Answer
Oct 6, 2016

Answer:

#x=1 and y=-7#

Explanation:

Given 2 equations, let us number them

#-16x-4y=12 #
we can simplify this equation by 4 , it would be easier for solving

#rArr(-16x-4y)/4=12/4#
#rArrcolor(blue)(-4x-y=3# equation1

the two equations are:

#color(blue)(-4x-y=3)#
#color(red)(-4x+y=-11)#

First we add both equations :
#color(blue)(-4x-y)color(red)(-4x+y)=3-11#
#-8x+0y=-8#
#-8x=-8#
#x=-8/-8#
#color(green)(x=1)#

second, let us substitute the value of #x# in equation 2
#color(red)(-4*1+y=-11)#
#rArr-4+y=-11#
#rArry=-11+4#
#color(green)(y=-7)#

Third, check if the values #color(green)(x=1 and color(green)(y=-7)# by substituting it in equation 1
#color(blue)(-4x-y=3)#
#color(blue)(-4(color(green)1)-(color(green)(-7))=?3)#
#color(blue)(-4+7=?3)#
#-3=?-3 true#

therefore,x=1 and y=-7#