Answer:
[tex]\left\{\begin{matrix}x+y=10\\ 0.05x+0.10y=0.85\end{matrix}\right.[/tex]
Step-by-step explanation:
System of Equations
Let's call:
x = number of nickels in the student's pocket
y = number of dimes in the student's pocket
Each nickel has a value of $0.05, so x nickels have a value of 0.05x
Each dime has a value of $0.10, so y dimes have a value of 0.10y
The student has a total of 10 coins, thus:
[tex]x+y=10[/tex]
The total value of the coins is $0.85, thus
[tex]0.05x+0.10y=0.85[/tex]
The system of linear equations that represents this scenario is:
[tex]\left\{\begin{matrix}x+y=10\\ 0.05x+0.10y=0.85\end{matrix}\right.[/tex]
