How do you solve 1/2(x-y) = 2 and 1/2(x+y)+1 = 0?

1 Answer
Apr 14, 2018

Answer:

#x=1# and #y=-3#

Explanation:

Solve like simultaneous equations.

Equation 1: #1/2(x-y) = 2#
Expand the brackets to get #1/2x-1/2y=2#

Equation 2: #1/2(x+y)+1 = 0#
Expand the brackets to get #1/2x+1/2y+1=0#

#1/2x-1/2y=2#

#1/2x+1/2y+1=0#

Add the two equations together to get
#1/2x+1/2x+1/2y-1/2y+1=2#

#x+1=2#
#x=1#

Substitute this value of #x# into either Equation 1 or 2 and solve for #y#

Equation 2: #1/2(1)+1/2y+1=0#
#1/2+1/2y+1=0#
#1/2y+1=-1/2#
#1/2y=-1##1/2#
#y = -3#