Question 1160616
let movies be {{{m}}} and video games {{{g}}}

if one month Michael rented {{{9}}} movies and {{{7 }}}video games for a total of ${{{56}}}, we have

{{{9m+7g=56}}}.........solve for {{{m}}}

{{{9m=56-7g}}}

{{{m=56/9-7g/9}}}........eq.1

if the next month he rented {{{3}}} movies and {{{5}}} video games for a total of ${{{34}}}, we have

{{{3m+5g=34}}}.........solve for {{{m}}}

{{{3m=34-5g}}}

{{{m=34/3-5g/3}}}........eq.2

from eq.1 and eq.2 we have

{{{56/9-7g/9=34/3-5g/3}}}.............solve for {{{g}}}, both sides multiply by {{{9}}} to get rid of fraction

{{{56-7g=34*3-5g*3}}}

{{{56-7g=102-15g}}}

{{{15g-7g=102-56}}}

{{{8g=46}}}

{{{g=5.75}}}

go to

{{{m=56/9-7g/9}}}........eq.1, substitute {{{g}}}

{{{m=56/9-(7*5.75)/9}}}
{{{m=56/9-40.25/9}}}
{{{m=6.222222222222221-4.472222222222222}}}
{{{m=1.75}}}


 the rental cost for each movie is ${{{1.75}}} and for each video game is ${{{5.75}}}