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.

<h3>Given information-</h3>

Emily has 8 coins in her purse totaling 50 cents

The only kinds of coins she has are nickels and dimes.

<h3>Nickel</h3>

A nickel is a coin which has the value equal to the 5 cents.

<h3>Dimes</h3>

A dimes is a coin which has the value equal to the 10 cents.

Suppose the number of nickel coin is <em>x </em>and the number of dimes coin is <em>y.</em>

As total coins are 8 . Thus,

$x+y=8$

$x=8-y$ ......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,

$5x+10y=50$

Put the value of the <em>x</em> from the equation 1 in the above equation.

$\begin{aligned}5(8-y)+10y &=50\\40-5y+10y &=50\\5y &=50-40\\y&=\dfrac{10}{5} \\y&=2\end$

Thus Emily have total 2 number of dimes coin.

Put this value of y in equation 1 we get,

$x=8-2\\x=6$

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;

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all radii of the same circle are congruent

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SSS congruency theorem

Step-by-step explanation: