Step-by-step explanation:
Let the cost of hot dog be [tex]hd[/tex]
Let the cost of hamburger be [tex]hm[/tex]
It is given that cost of three hot dogs and four hamburgers is $13.25
So, [tex]3\times hd+4\times hm=13.25[/tex] .....[tex](i)[/tex]
It is given that cost of four hot dogs and three hamburgers is $13.00
So,[tex]4\times hd +3\times hm=13[/tex] .....[tex](ii)[/tex]
[tex]4\times (ii)-3\times (i)\text{ gives,}[/tex]
[tex]4\times(4\times hd+3\times hm)=4\times 13\\-3\times(3\times hd+4\times hm)=3\times 13.5\\\\7\times hd=11.5\\hd=1.64[/tex]
Substitute [tex]hd[/tex] in [tex](ii)[/tex] to get [tex]hm[/tex],
[tex]4\times 1.64 + 3\times hm=13\\3\times hm=6.43\\hm=2.14[/tex]
Hence cost of hot dog is $1.64 and cost of hamburger is $2.14