The cost of an order of 1 hamburger and 2 orders of fries cost which Nathaniel and Liam bought is $6.5.
A system of equation is the set of equation in which the finite set of equation is present for which the common solution is sought.
Let the cost of 1 hamburger is x dollar and 2 orders of fries is y dollars. Nathaniel bought 3 hamburgers and 2 orders of fries for $12.50. Thus,
[tex]3x+2y=12.5[/tex]
Solve this equation as,
[tex]2y=12.5-3x\\y=\dfrac{12.5-3x}{2}[/tex] .....1
Liam bought 2 hamburgers and 4 orders of fries for $13. Thus,
[tex]2x+4y=13[/tex]
Put the value of y in this equation and solve it further,
[tex]2x+4(\dfrac{12.5-3x}{2})=13\\2x+25-6x=13\\-4x=13-25\\-4x=12\\x=\dfrac{12}{4}\\x=3[/tex]
Put this value of x in equation 1,
[tex]y=\dfrac{12.5-3\times3}{2}\\y=\dfrac{3.5}{2}\\y=1.75[/tex]
The cost of an order of 1 hamburger and 2 orders of fries is,
[tex]C=3\times 1+2\times1.75\\C=3+3.5\\C=6.5[/tex]
Thus, the cost of an order of 1 hamburger and 2 orders of fries cost which Nathaniel and Liam bought is $6.5.
Learn more about the system of equations here;
https://brainly.com/question/13729904
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