Teaching Notes 4.17: Graphing Systems of Linear Equations
When Lines Intersect
Systems of linear equations can be solved in several ways, one of which is by graphing. To
successfully solve systems of linear equations by graphing, students must first understand how to
graph equations and recognize the point of intersection as the solution to the system.- Explain that one way to solve a system of linear equations is to graph each equation and find
the point of intersection. - Explain the basic steps for graphing a linear equation:
- Students may use thex-andy-intercepts to graph a linear equation or they may graph
they-intercept and then move vertically and horizontally, depending on the slope, and
then graph the second point. - Students should draw a line connecting the two points.
- Students may use thex-andy-intercepts to graph a linear equation or they may graph
- Review the information and example on the worksheet with your students. Note that a solu-
tion to a system of equations is represented by the point where the graphs intersect, an
ordered pair (x,y) that satisfies each equation in the system.
EXTRA HELP:
Check solutions algebraically by substituting each value into the original system of equations.ANSWER KEY:
(1)(2, 12) (2)(−5, 1) (3)(1, 1) (4)(−2, 7) (5)(2,−1) (6)(−4, 5) (7)(10, 5) (8)(3,−5)
------------------------------------------------------------------------------------------
(Challenge)The graphing method may still be used to solve systems of equations when the
solutions are not integers; however, it is not the best method because the values forxandymust
be estimated. Substitution, addition or subtraction, or multiplication with addition or subtraction,
would be better methods to solve these problems.
------------------------------------------------------------------------------------------170 THE ALGEBRA TEACHER’S GUIDE