# MPM2D - Linear Relations ```01a3 Solving Graphically.notebook
February 08, 2016
Unit 1 &shy; Systems of Linear Equations
Feb 6&shy;11:29 PM
Consider:
A linear relation can be represented graphically
as a straight line.
A straight line is made up of an infinite number
of points, (x, y), connected together.
Some other straight line would be made up of
an infinite number of different points.
What does it mean for these lines to intersect?
Sep 13&shy;10:53 PM
1
01a3 Solving Graphically.notebook
February 08, 2016
Unit 1 &shy; Systems of Linear Equations
Solving Linear Systems Graphically
The graph of a linear relation forms a straight line.
Two (or more) linear relations can be graphed together,
forming a linear system.
The solution to a linear system is the point (x,y) where
the lines intersect (or cross) each other.
line b
Point of
Intersection
(solution)
line a
solve graphically
a)
Feb 9&shy;8:53 PM
2
01a3 Solving Graphically.notebook
February 08, 2016
a)
Feb 9&shy;8:53 PM
b)
Feb 9&shy;8:54 PM=
3
01a3 Solving Graphically.notebook
February 08, 2016
b)
Not all solutions will have 'nice' values.
These can be difficult, or impossible, to solve
graphically.
Feb 9&shy;8:54 PM=
c)
#3, #4
4
01a3 Solving Graphically.notebook
February 08, 2016
c)
#3, #4
d)
#1, #2
5
01a3 Solving Graphically.notebook
February 08, 2016
d)
#1, #2
In Summary:
For no solution:
&shy; same slope and different y&shy;intercepts
For exactly one solution:
&shy; different slopes only
&shy; some graphical systems can only
be solved exactly using technology
For infinitely many solutions:
&shy; same slope and same y&shy;intercept
summary
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01a3 Solving Graphically.notebook
February 08, 2016
Assigned Work:
p. 26 # 2(i)(abc), 3ab, 5abf, 10, 18*
hw
7
Attachments
Basic 2D Grid.agg
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