We are told the costs of jars of jam and packages of bread in a gift basket.
We will write a system of equations representing this situation. Let x represent the number of jars of jam and let y represent the packages of bread in the basket. We can write our first equation because we know that the total number of items in the basket is 8.
x+y= 8The cost of one jar of jam is $6. To find out how much the jars of jam are worth, we need to multiply the number of jars x by the cost of one jar. We can do the same for packages of bread which cost $5 each.
Cost of Jars of Jam:&& x* $6
Cost of Packages of Bread:&& y* $5
Now, we can write our second equation knowing that the whole basket costs $45.
x* $6+y* $5= $45
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= 8 & (I) 6x+ 5y= 45 & (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=8 & (I) 6x+ 5y=45 & (II)
Currently, none of the terms in this system will cancel out. However, if we multiply Equation (I) by - 5 the y-terms will have opposite coefficients.
-5(x+y)=-5(8) 6x+ 5y=45
⇓
- 5x-5y=- 40 6x+ 5y=45
Now the y-terms will eliminate each other if we add Equation (II) to Equation (I). Let's do this!
