Education Technology

Expressions and Equations / What is a solution to a System of Equations

Grade Level 8
Activity 16 of 18
In this lesson students are introduced to a system of linear equations in two variables and find solutions using balances. Then students investigate graphically systems with a unique solution, no solutions, or infinitely many solutions.

Planning and Resources

Students should be able to identify whether the solution to a system of two linear equations is a point, all points on a line, or there is no solution. They should also be able to describe the solution in terms of the graphs of the two equations, and identify characteristics of equations that will lead to each possible outcome.

system of linear equations in two variables
parallel lines
solution to a system of two linear equations

Standard: Search Standards Alignment


Lesson Snapshot


Students understand that the solution to a system of two linear equations is the intersection of the graphical representation of the two equations.

What to look for

Students make the connection between the \((x, y)\) pair that makes each equation true and the point of intersection of the two lines.

Sample Assessment

Joe solved this linear system correctly.

These are the last two steps of his work

Which statements about this linear system must be true?

a. \(x\) must equal 6
b. \(y\) must equal 6
c. There is no solution to this system
d. There are infinitely many solutions to this system

Answer: d

The Big Idea

Some systems of linear equations in two variables have one point as a solution, some have no points as a solution, and some have infinitely many points as a solution.

What are the students doing?

Students reason about solutions to systems of two linear equations using balance beams.

What is the teacher doing?

Encourage students to build on the knowledge that all of the points \((x, y)\) that make \(ax+by = c\) a true statement lie on a line, and recognize that the solution, if one exists, would be the pair \((x, y)\) that makes both statements true.