Question 1152499
eggs have {{{6 }}}grams of protein and {{{77}}} calories:
milk has {{{8}}} grams of protein and {{{168}}} calories


if the number of eggs is {{{x}}} and the number of glasses of milk {{{y}}}

 eggs have {{{6 }}}grams=>{{{6x}}} grams of protein and {{{77x}}} calories
milk have {{{8 }}}grams=>{{{8y}}} grams of protein and {{{168y}}} calories
to keep alive you must consume {{{36}}} grams of protein and{{{ 658}}} calories per day
{{{36}}} grams of protein :

{{{6x+8y=36}}}.............eq.1

{{{ 658}}} calories :

{{{77x+168y=658}}}............eq.2

solve the system:

{{{6x+8y=36}}}.............eq.1
{{{77x+168y=658}}}............eq.2
----------------------------------------------------------

start with
{{{6x+8y=36}}}.............eq.1.....solve for {{{y}}}
{{{8y=36-6x}}}
{{{y=36/8-6x/8}}}
{{{y=4.5-0.75x}}}......eq.1a

substitute in eq.2

{{{77x+168(4.5-0.75x)=658}}}............eq.2....solve for {{{x}}}

{{{756-49x=658}}}
{{{756-658=49x}}}
{{{98=49x}}}
{{{x = 2}}}

go to eq.1a

{{{y=4.5-0.75x}}}......eq.1a, substitute {{{2}}} for {{{x}}} and solve for {{{y}}}

{{{y=4.5-0.75*2}}}
{{{y=4.5-1.5}}}
{{{y = 3}}}


you   must consume {{{2}}} eggs and {{{3}}} glasses of  milk  each day to stay alive 

check:calories

{{{2*77+3*168=658}}}
{{{154+504=658}}}
{{{658=658}}}

check: proteins

{{{6*2+8*3=36}}}
{{{12+24=36}}}
{{{36=36}}}