How do you solve the system using the elimination method for 2x+y=7 and x+2y=11?

1 Answer
Aug 1, 2015

Answer:

#(x,y) = (1,5)#
#color(white)("XXXX")#(see below for solution by substitution)

Explanation:

[1]#color(white)("XXXX")##2x+y=7#
[2]#color(white)("XXXX")##x+2y = 11#

Multiply both sides of [1] by #2# so we have 2 equations with #y# having a coefficient of #2#
[3]#color(white)("XXXX")##4x+2y=14#

Subtract [2] from [3] eliminating the #y# term
[4]#color(white)("XXXX")##3x = 3#

Divide both sides by #3#
[5]#color(white)("XXXX")##x = 1#

Substitute #1# for #x# in [2]
[6]#color(white)("XXXX")##1+2y=11#
Subtract #1# from both sides
[7]#color(white)("XXXX")##2y = 10#
Divide both sides by #2#
[8]#color(white)("XXXX")##y=5#