Properties of Linear Equations

1
Properties of Linear Equations
This will probably be a little bit boring!
2
Properties of Linear Equations
y x y -2x 3
This system has one solution (one intersection),
so it is called consistent.
3
Properties of Linear Equations
y x y x 3
This system has no solutions (no intersection),
so it is called inconsistent. In inconsistent
linear equations, we have 2 parallel lines.
4
Properties of Linear Equations
y x 3 2y 2x 6
You should notice that the second equation is the
first equation, but everything is multiplied by
two. This equation has infinitely many
solutions. It is also consistent. These two
equations are colinear.
5
Properties of Linear Equations
So, systems of two linear equations may have 0, 1
or 8 roots.
6
System y x 2 y x 3
System 2y 2x 4 5y 5x 15
Multiplying both sides of either equation of a
linear system by a constant does not change the
solution.
7
System y x 2 y 2x 3
Lets add y x 2 y 2x 3 2y 3x 5
Adding (or subtracting) two linear equations does
not change the solution. The new line goes
through the same point as the original two lines!
8
There you have it!
Exercise 3.4 Handout (also found on p.
147) Your mission, if you choose to accept it,
and also if not, is to complete Exercises 1-5 on
page 147. Mr. Plett will select 3 questions from
1-5 that must be handed in for marks on Monday at
the beginning of class.