If students struggle to write equations in the first question, ask them how they might find out Jada's earnings if she works 1 hour, 2 hours, 5 hours, and so on. Then, ask them to generalize the computation process for hours.

Ask a student to share the equation that represents Jada earning $90.45. Make sure students understand why describes that constraint. 

Next, invite students to share how they knew if 4 and 7 are or are not solutions to the equation. Highlight that substituting those values into the equation and evaluating them lead to false equations. 

Then select students using different strategies to share how they found the solution. Some students might notice that the solution must be greater than 7 (because when , the expression has a value less than 90.45) and start by checking if is a solution. If no students mention this, ask them about it. 

Make sure students understand what the solution means in context. Emphasize that 8 is the number of hours that meet all the constraints in the situation. Jada gets paid $12.20 an hour, pays $7.15 in bus fare, and takes home $90.45. For all of these to be true, she must have worked 8 hours.

The goal of the discussion is to make sure students understand that a solution to an equation in two variables is any pair of values that, when substituted into the equation and evaluated, make the equation true. Discuss questions such as:

• “In this situation, what does it mean when we say that and is not a solution to the equation?” (It is not a combination of gasoline and ethanol that would produce 100 pounds of carbon dioxide. Substituting them for the variables in the equation leads to a false equation of .) 
• “How did you find out the gallons of ethanol burned in the engine given that 4 gallons of gasoline were burned?” (Substitute 4 for , and solve the equation.)
• “Can you find another combination that is a solution?”
• “How many possible combinations of gallons of gasoline and ethanol (or and ) would add up to 100 pounds of carbon dioxide?” (Many solutions) 

As a segue to the next lesson, solicit some ideas on how we know that there are many solutions to the equation. If no one mentions using a graph, bring it up and tell students that they will explore the graphs of two-variable equations next.