Unit 5, Lesson 11
Solutions to Linear Equations
Accelerated 7
Preparation
Lesson Narrative
In this lesson, students find solutions to an equation with two variables: pairs of numbers that make the equation and situation true. They look at contexts where both variables have to satisfy a constraint, often represented with an equation of the form .
Students consider two situations. The first looks at different ways of spending \$10 on two differently priced fruits. The second looks at pairs of numbers where twice the first number plus the second number adds up to 10. While the constraints for these two situations result in two equivalent equations, creating the graphs representing each requires students to interpret the meaning of their solutions in a context (MP2). For example, the graph representing the two numbers is a straight line that includes positive and negative numbers, while the graph representing the fruit is a set of discrete points that lie on the same line and must be positive whole numbers.
Students also consider pairs of numbers that do not make the equation or situation true, observing that those points do not lie on the graph.
- Create a graph and an equation in the form $Ax+By=C$ that represent a linear relationship.
- Describe that for the graph and equation of the same line, every point on the line is a solution to the equation, and any point not on the line is not a solution to the equation.
- Determine pairs of values that satisfy or do not satisfy a linear relationship using an equation or graph.
Let’s think about what it means to be a solution to a linear equation with two variables in it.