How do you solve the following system: #2x+y=5, 5x+2y=12 #?

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Answer 1 · 2016-03-26T02:13:40

#x=2#
#y=1#

Given -

#2x+y=5# ---------------(1)
#5x+2y=12#-------------(2)

Solve equation (1) for #y#

#y=5-2x#

Substitute #y=5-2x# in equation (2)

#5x+2(5-2x)=12#

Simplify and find the value of #x#

#5x+10-4x=12#
#x=12-10#
#x=2#

Substitute #x=2# in equation (1) and find the value of #y#

#2(2)+y=5#
#4+y=5#
#y=5-4#
#y=1#
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