Question 652169
given:

Joe buys {{{5}}} shirts and {{{3}}} shorts for ${{{51}}}.

Bill buys {{{3}}} shirts and {{{7}}} shorts for ${{{80}}}.

if{{{ x}}} is cost of each shirt and if {{{y}}} is the cost of each pair of shorts, than we have:

{{{ 5x+3y=51}}}....1....what Joe buys

{{{ 3x+7y=80}}}....2....what Bill buys
____________________________________.....solve the system

{{{ 5x+3y=51}}}....1...solve for {{{x}}}

{{{ 5x=51-3y}}}

{{{ x=51/5-3y/5}}}..........plug it in 2 and solve for {{{y}}}

{{{ 3(51/5-3y/5)+7y=80}}}....2

{{{ 153/5-9y/5+7y=80}}}....each term multiply by {{{5}}}

{{{ 153*5/5-9*5y/5+7*5y=80*5}}}

{{{ 153*cross(5)/cross(5)-9*cross(5)y/cross(5)+35y=400}}}

{{{ 153-9y+35y=400}}}

{{{ 26y=400-153}}}

{{{ 26y=247}}}

{{{ y=247/26}}}

{{{ highlight(y=9.5)}}}..........cost of each each pair of shorts

now find {{{x}}}

{{{ x=51/5-3y/5}}}

{{{ x=10.2-3(9.5)/5}}}

{{{ x=10.2-28.5/5}}}

{{{ x=10.2-5.7}}}

{{{ highlight(x=4.5)}}}......cost of each shirt