The previous lesson focused on the relationship between a linear equation in two variables, its solution set, and its graph. These themes continue to develop in this lesson. In the first activity after the warm-up, students analyze statements about a collection of three graphs, deciding whether or not certain ordered pairs are solutions to the equations defining the lines. In particular, students realize that values \(x = a\) and \(y = b\) satisfy two different linear equations simultaneously when the point \((a,b)\) lies on both lines represented by the equations. This is important preparation for thinking about what it means to be a solution to a system of equations in the next unit.
In the second activity, students consider equations given in many different forms, ask their partner for either the \(x\)- or \(y\)-coordinate of a solution to the equation, and then give the other coordinate. This activity prepares students for finding solutions to systems of equations, because it gets them to look at the structure of an equation and decide whether it would be easier to solve for \(y\) given \(x\), or to solve for \(x\) given \(y\) (MP7).
- Calculate the solution to a linear equation given one variable, and explain (orally) the solution method.
- Determine whether a point is a solution to an equation of a line using a graph of the line.
Let’s find solutions to more linear equations.
One copy of the I’ll Take an X Please blackline master for every pair of students.
- I can find solutions $(x, y)$ to linear equations given either the $x$- or the $y$-value to start from.
solution to an equation with two variables
A solution to an equation with two variables is a pair of values of the variables that make the equation true.
For example, one possible solution to the equation \(4x+3y=24\) is \((6,0)\). Substituting 6 for \(x\) and 0 for \(y\) makes this equation true because \(4(6)+3(0)=24\).
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