Question 734854
let hotdogs be {{{x}}} and hamburgers {{{y}}}

if five hotdogs and two hamburgers cost ${{{10.25}}}, then

{{{5x+2y=10.25}}}.....eq.1

if two hotdogs and five hamburgers cost ${{{12.50}}},then

{{{2x+5y=12.50}}}.....eq.2

now solve this system:


{{{5x+2y=10.25}}}.....eq.1
{{{2x+5y=12.50}}}.....eq.2
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{{{5x+2y=10.25}}}.....eq.1....solve for {{{x}}}

{{{5x=10.25-2y}}}

{{{x=10.25/5-2y/5}}}

{{{x=2.05-0.4y}}}......plug it in eq.2


{{{2(2.05-0.4y)+5y=12.50}}}.....eq.2..solve for {{{y}}}


{{{4.1-0.8y+5y=12.50}}}

{{{-0.8y+5y=12.50-4.1}}}

{{{4.2y=8.4}}}

{{{y=8.4/4.2}}}

{{{highlight(y=2)}}}........hamburger cost

now find {{{x}}}

{{{x=2.05-0.4*2}}}

{{{x=2.05-0.8}}}

{{{highlight(x=1.25)}}}.....hotdog cost


check:

{{{5x+2y=10.25}}}.....eq.1
{{{5*1.25+2*2=10.25}}}
{{{6.25+4=10.25}}}
{{{10.25=10.25}}}


{{{2x+5y=12.50}}}.....eq.2
{{{2*1.25+5*2=12.50}}}
{{{2.50+10=12.50}}}
{{{12.50=12.50}}}