# Solving Systems Word Problems

Her sister earned 0 by working 15 hours during the week and 10 hours on the weekend.What was the hourly pay rate for working weekdays and weekends?

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We'll need to use different variables to represent each unknown.

Let's use x for the weekday rate and y for the weekend rate.

We can use c to represent the price for a box of cookies and p to represent the price for a bag of popcorn.

Next we can use the information in the word problem to set up equations that will help us find the values of the variables.The first equation can be solved for y by subtracting 22x from both sides of the equation. Since y is equal to the expression 232 - 22x, we can substitute the expression for y in the second equation.Thus, the equation becomes 15x 10 (232 - 22x) = 270.We can represent this with the equation 22x y = 232.Using the pay for the other cousin, we get the equation 15x 10y = 270.In this lesson, you'll use systems of equations and solve word problems that have more than one unknown value.Systems of equations have two or more equations with two or more variables that are solved simultaneously.The first day, the soccer team sold 44 bags of popcorn and 32 boxes of cookies for a total of .We can represent this with the equation 44p 32c = 97.Since there are two equations with the same two variables, we can set them up as a system of equations and solve them simultaneously.The system of equations can be solved using the substitution method, which involves using an expression from one equation to substitute for one of the variables in the other equation.

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