Question 994723
let  ribeye steak dinners be {{{x}}} and grilled salmon dinners {{{y}}}

if a waitress sold {{{17}}} ribeye steak dinners and {{{20}}} grilled salmon dinners, totaling ${{{590.81}}} on a particular day, then we have

{{{17x+20y=590.81}}}.........eq.1

if another day she sold {{{24}}} ribeye steak dinners and {{{10}}} grilled salmon dinners, totaling ${{{580.66}}},  then we have

{{{24x+10y=580.66}}}.........eq.2

solve the system:

{{{17x+20y=590.81}}}.........eq.1
{{{24x+10y=580.66}}}.........eq.2...=> both sides multiply by {{{2}}}
-------------------------------------------

{{{17x+20y=590.81}}}.........eq.1
{{{48x+20y=1161.32}}}.........eq.2=> subtract eq.1 from eq.2
-----------------------------------------------------

{{{48x+20y-(17x+20y)=1161.32-590.81}}}

{{{48x+cross(20y)-17x-cross(20y)=570.51}}}

{{{48x-17x=570.51}}}

{{{31x=570.51}}}

{{{x=570.51/31}}}

{{{x=18.40354838709677}}}

{{{highlight(x=18.40)}}}

now find {{{y}}}

{{{24x+10y=580.66}}}.........eq.2

{{{24*18.40354838709677+10y=580.66}}}

{{{441.68516129032248+10y=580.66}}}

{{{10y=580.66-441.68516129032248}}}

{{{10y=138.97483870967752}}}

{{{y=138.97/10}}}

{{{highlight(y=13.89)}}}

How much did each type of dinner cost?
 ribeye steak dinners cost {{{highlight(18.40)}}} and 
grilled salmon dinners cost {{{highlight(13.89)}}}