Question 1195779


let motorcycles (2 wheels)  be {{{x}}} and cars (4 wheels) {{{y}}}
if there are 35 vehicles we have 

{{{x+y=35}}}...........eq.1 

if there 114 wheels, we have

{{{2x+4y=114}}}...........eq.2

solve the system
{{{x+y=35}}}...........eq.1 
{{{2x+4y=114}}}...........eq.2
-------------------------------------------ultiply eq1 by {{{4}}}
{{{4x+4y=140}}}...........eq.1 
{{{2x+4y=114}}}...........eq.2
-------------------------------------------- subtrat eq2 fro eq1 to eliinate {{{y}}}

{{{4x+4y-(2x+4y)=140-114}}}

{{{4x+4y-2x-4y=26}}}

{{{ 2x=26}}}

{{{ x=13}}}

go to 
{{{x+y=35}}}...........eq.1 substitute {{{x}}}

{{{13+y=35}}}

{{{y=35-13}}}

{{{y=22}}}


there are {{{13}}} motorcycles and {{{ 22}}} cars