Download Linear Equations in Two Variables

Linear Equations in Two Variables
A linear equation is an equation of the form.
Notice that this equation has
variables:
and .
Consider the equation:
- The
- The
- The
term is
term is
term is
This equation has an infinite number of solutions and these
solutions are expressed as Ordered Pairs written in the form (
Order is very important, hence the name Ordered Pairs. The
always first and the is always second.
).
is
To find some solutions to the equation
We make a chart:
To fill out the “ ” column, we
substitute for and solve for .
If
, we have
( )
1
So we can fill out the chart
As an ordered pair, we write this solution (
when
,
.
) indicating that
Consider the equation:
To find ordered pairs that satisfy this equation we set up a
chart:
Fill in the corresponding
values
NOTE: We can choose any value for and find its corresponding value, but it is helpful to choose small, whole numbers to make the
calculations a bit easier.
2
Example 1:
Find three solutions to the equation
Plotting Solutions
Consider the equation
The solution to this single variable equation is
.
We can plot this solution on a number line:
𝟑
𝟐
𝟏
𝟎
𝟏
𝟐
𝟑
Since linear equations have two variables, we require two
number lines to plot solution points.
𝒚-axis
𝒙-axis
3
Cartesian Coordinate System
Origin (
Quadrant
)
Quadrant
Quadrant
Quadrant
This coordinate system is known as the Cartesian coordinate system.
) is called the origin and denotes the solution
The point (
when
.
The Cartesian coordinate system is made up of
above.
4
quadrants labeled
Example 2:
Plot the following points on the graph above:
a.) (3, 2)
b.) (-2, 1)
c.) (6, -2)
d.) (-4, -3)
e.) (0, 0)
5
Linear Equations in
Two Variables
Practice Problems
1.
Find at least
2.
Does the point (–
) satisfy the equation
3.
Does the point (–
) satisfy the equation
4.
Plot the following points on the graph below:
a.) (–
b.) (
solutions to the linear equation
)
c.) (
d.) (
)
6
?
?
)
)