Transcript Tutorial 14a - C on T ech Math : : An application

Solving Systems of Linear Equations
Tutorial 14a
A Solution Set

Consider the different meanings of the word
solution.
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The solution to the mystery escaped him.
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The town’s solution to its landfill problem is to
encourage recycling.
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The word solution here refers to an explanation.
Solution here refers to a method of solving a problem.
A chemist mixes two solutions to obtain a 15%
acid solution.
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Solution here refers to a homogeneous molecular
mixture
Solution Set
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In Mathematics we also have different
kinds of solutions and, therefore,
different kinds of solution sets.
Study the table below:
Equation/Inequality
3x + 5 = 14
|x|  5
x+3=x-7
(x + 6)(x – 3)=0
Solution Set
{3}
{-5  x  5}
No Solution
{-6, 3}
These examples
illustrate that a
solution set may have
one member, more
than one member, or
no members.
Systems of Linear Equations
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Two or more linear equations in the same
variables form a system of linear equations.
The graphs of y = ½x and x + y = 6 are
shown at the bottom right.
The ordered pair of the point at which the
lines intersect is called the solution to the
6•
system.
4
2
-6 -4 -2
•
-2
-4
-6
•
2
•(4, 2)
4
•6
Systems of Linear Equations
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The graphs of y = ½x and x + y = 6 are
shown at the bottom right.
Together these two equations form a system
of linear equations.
Below you can see that the coordinate (4,2)
6•
satisfies both equations.
Equations
y = ½x
x+y=6
Check (4,2)
2 = ½•4
4+2=6
4
True or False?
True
True
2
-6 -4 -2
•
-2
-4
-6
•
2
•(4, 2)
4
•6
Solving Systems of Equations
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To solve a systems of equations means
to find the coordinates of the point(s) of
intersection of the graphs of the two
equations.
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A system whose graphs intersect at one
point has one solution.
A system whose graphs are parallel has no
solution
A system whose graphs coincide has
infinitely many solutions.
3 Methods to Solve
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There are 3 methods that we can use to
solve systems of linear equations.
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Solve by the Graphing Method
Solve by the Substitution Method
Solve by the Addition (Elimination) Method