With this problem our goal is to get two equations in the form of A*x* + B*y* = C where *x *is the price of renting a movie and *y *the price of renting a video game. A, B, and C are simply constants, or numbers that won't change in value. Once we have two equations, we can use them to solve for *x* and *y*.

**1) **Write the equation for Elsa's first month

If *x* is the price of renting a movie and Elsa rents two movies, her movie rental cost comes out to 2*x *(number of movies multiplied by the price of each movie). Similarly, for video games costing *y* dollars to rent, her cost is 3*y*. Her total is $26 which means her movie cost (2*x*) and her video game cost (3*y*) together come to $26. This gives us 2*x* + 3*y* = $26

**With just one equation and two variables, we can't solve for either variable. We need a second equation.**

**2) **Write the equation for Elsa's second month

Following the same steps we took to write the first equation, we get 6*x* + 5*y* = $56

**Now we have two equations with the same two variables, we can use those equations to solve both variables.**

**3)** Using either equation, solve for one of the variables

Now, we want to isolate a variable. Looking at the first equation, let's solve for *x*. Solving for *x* gives us: *x* = (26 - 3*y*) / 2

**4)** Solve for the other variable by substitution

Now that we have a value for *x *in terms of *y*, we can substitute that in for *x* in the second equation to give us one equation with one variable. It should look like: 6 (26 - 3*y*)/2 + 5*y* = 56. With some algebra, we simplify down to 78 -9*y* + 5*y* = 56 and further to -4*y* = -22. That's an easy solve for *y*. Divide -22 by -4 to get $5.50 for the cost of renting a video game.

**5) **Substitute the solved variable's value into the equation

Almost done! Plug in the value of *y* into either equation and then solve for *x*. Returning to the first equation, we get 2*x* + 3($5.50) = $26 or, 2*x* + $16.50 = $26. Now with one variable and one equation *x* = $______

(*x* = $4.75)

**6)** Check your work.

Plug both values into the other equation and make sure they make sense. Taking the second equation, we get 6($4.75) + 5($5.50) = $56. Awesome!