We are given some information about the coins in our pocket. We will write a system of equations representing this situation. Let x represent the number of nickels and let y represent the number of dimes in our pocket. We can write our first equation because we know that the total number of coins in our pocket is 10.
x+y= 10
A nickel is worth $0.05. To find out how much our total number of nickels is worth, we need to multiply the number of nickels x by the monetary value of one nickel. We can do the same for dimes which are worth $0.10.
Value of Our Nickels:&& x* $0.05
Value of Our Dimes:&& y* $0.10Now, we can write our second equation knowing that the total value of coins in our pocket is $0.70.
x* $0.05+y* $0.10= $0.70
Next, we can create a system of equations by combining the two equations and making them into one system. For simplicity, we will remove the dollar signs from the second equation.
x+y= 10 & (I) 0.05x+ 0.1y= 0.7 & (II)
To solve this system we will use the Elimination Method. When using the Elimination Method, one of the variable terms needs to be eliminated when one equation is added to or subtracted from the other. This means that either the x- or the y-terms must cancel each other out.
x+y=10 & (I) 0.05x+ 0.1y=0.7 & (II)
Currently, none of the terms in this system will cancel out. However, if we multiply Equation (II) by - 10, the y-terms will have opposite coefficients. Let's do this!
