Advanced Algebra Notes
SECTION 3.1
SOLVING LINEAR
SYSTEMS BY GRAPHING
Solving Linear Systems by Graphing
System of two linear equations
A
in two
variables x and y, also called linear system, consists of
two equations that can be written in the following
form.
Ax + By = C
Dx + Ey = F
solution
When we talk about finding a
we
are looking for the ordered pair (x,y) that will satisfy
each equation. It must work with both!
Example 1
Graph the linear system and estimate the solution. Then check the
solution algebraically.
4x+y=8
2x-3y=18
𝑦 = −4𝑥 + 8
(3, −4)
Example 2
Graph the linear system and estimate the solution.
4x-3y=8
8x-6y=16
−3𝑦 = −4𝑥 + 8
4
8
𝑦= 𝑥−
3
3
−6𝑦 = −8𝑥 + 16
−3𝑦 = −4𝑥 + 8
4
8
𝑦= 𝑥−
3
3
Example 3
Graph the linear system and estimate the solution
2x+y=4
2x+y=1
𝑦 = −2𝑥 + 4
𝑦 = −2𝑥 +1
When lines have the same slope
they are parallel. They will not cross!
They will not have a solution!
Example 4
Graph the linear system and estimate the solution
5x-2y=-10
2x-4y=12
−2𝑦 = −5𝑥 − 10
5
10
𝑦= 𝑥+
2
2
5
𝑦 = 𝑥+5
2
−4𝑦 = −2𝑥 + 12
1
𝑦 = 𝑥−3
2
(−4, −5)
Closing: How do you solve a system of linear
equations graphically?
Our solution is the point where our lines
intersect. It is a coordinate point (𝑥, 𝑦)
If our lines do not cross, they are parallel
meaning they have no solution.
If our lines are the same line, they are
Intersect at every point meaning they
have infinite solutions.
Our solution has to work for both equations!!!