Respuesta :
Linear equation are the equation which has the power of the unknown variable is 1. The Emily have total 2 number of dimes coin and total 6 number of nickels coin.
Given information-
Emily has 8 coins in her purse totaling 50 cents
The only kinds of coins she has are nickels and dimes.
Nickel
A nickel is a coin which has the value equal to the 5 cents.
Dimes
A dimes is a coin which has the value equal to the 10 cents.
Suppose the number of nickel coin is x and the number of dimes coin is y.
As total coins are 8 . Thus,
[tex]x+y=8[/tex]
[tex]x=8-y[/tex] ......equation 1
As the total value of the cents is 50 and nickel is equal to the 5 cents whereas the dimes is equal to the 10 cents. Thus,
[tex]5x+10y=50[/tex]
Put the value of the x from the equation 1 in the above equation.
[tex]\begin{aligned}5(8-y)+10y &=50\\40-5y+10y &=50\\5y &=50-40\\y&=\dfrac{10}{5} \\y&=2\end[/tex]
Thus Emily have total 2 number of dimes coin.
Put this value of y in equation 1 we get,
[tex]x=8-2\\x=6[/tex]
Thus Emily have total 6 number of nickels coin.
Hence the Emily have total 2 number of dimes coin and total 6 number of nickels coin.
Learn more about the coin based problems here;
https://brainly.com/question/10482015
