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Lesson: Solving Systems of Linear Equations Graphically Mathematics • 8th Grade

In this lesson, we will learn how to solve a system of two linear equations by considering their graphs and identifying the point of intersection.

Lesson Plan

Students will be able to

  • understand that the solution set of a system of equations is graphically represented by the point or points at which the lines intersect,
  • understand the possible solution cases when solving a system of linear equations, particularly that
    • an independent system of linear equations (nonparallel lines) has one solution,
    • a dependent system of linear equations (coincident lines) has an infinite number of solutions,
    • an inconsistent system of linear equations (parallel lines) has no solution,
  • identify how many solutions a system of linear equations has when given the graph of the system,
  • find the solutions to a system of linear equations when given the graph of the system, the graph and the two equations, the graph only, or the two equations only (by constructing a graph).

Lesson Presentation

Lesson Video

Video Thumbnail
15:13

Lesson Explainer

Lesson Playlist

Lesson Worksheet

Q1:

Answer the questions for the lines 𝑦=3π‘₯βˆ’2 and 𝑦=βˆ’2π‘₯βˆ’2.

Substitute π‘₯=0 into the equation 𝑦=3π‘₯βˆ’2 and state the corresponding value of 𝑦.

Substitute π‘₯=0 into the equation 𝑦=βˆ’2π‘₯βˆ’2 and state the corresponding value of 𝑦.

The given graph shows the lines 𝑦=3π‘₯βˆ’2 and 𝑦=βˆ’2π‘₯βˆ’2. What do you notice about the point (0,βˆ’2)?

Therefore, determine the point whose coordinates are solutions to the system of equations 𝑦=3π‘₯βˆ’2 and 𝑦=βˆ’2π‘₯βˆ’2.

Q2:

Do the simultaneous equations plotted in the given graph have a solution? If yes, find it.

Q3:

Find the solution set of the two equations represented by 𝐿 and 𝐿.

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