Education Technology

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

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

Objectives
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.

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

Standard:

## Lesson Snapshot

#### Understanding

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.
$$6x+3y=6$$
$$y=2x+2$$

These are the last two steps of his work
$$6x-6x+6=6$$
$$6=6$$

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

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.