How do you solve the following system?: #2x +y = 13 , 3x +2y = -2#

2 Answers
Jan 23, 2016

Answer:

#(x,y)=(28,-43)#

Explanation:

Given:
[1]#color(white)("XXX")2x+y=13#
[2]#color(white)("XXX")3x+2y=-2#

Multiply [1] by #2# to give #y# a coefficient equal to that in [2]
[3]#color(white)("XXX")4x+2y=26#

Subtract [2] from [3] to eliminate the #y# term
[4]#color(white)("XXX")x=28#

Substitute #28# for #x# back into [1]
[5]#color(white)("XXX")2xx28 +y=13#

Simplify
[6]#color(white)("XXX")y=13-56 = -43#

Jan 23, 2016

Answer:

#x=28#
#y=-43#

Explanation:

Given -

#2x+y=13# ---------------------------(1)
#3x+2y=-2# ---------------------------(2)

Solve equation (1) for #y#

#y=13-2x#

Substitute #y=13-2x# in equation (2)

#3x +2(13-2x)=-2#
#3x+26-4x=-2#
#-x+26=-2#
#-x=-2-26#
#-x=-28#
#x=28#

Substitute #x=28# in equation (1)

#2(28)+y=13#
#56+y=13#
#y=13-56=-43#
#y=-43#