Solving Systems of Equations

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Solving Systems of Equations 3 Approaches
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Mrs. N. Newman
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Method 1 Graphically
Door 1
Method 2 Algebraically Using Addition and/or
Subtraction
Door 2
Method 3 Algebraically Using Substitution
Door 3
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In order to solve a system of equations
graphically you typically begin by making sure
both equations are in standard form.
Where m is the slope and b is the y-intercept.
Examples y 3x- 4 y -2x 6
Slope is 3 and y-intercept is - 4.
Slope is -2 and y-intercept is 6.
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Graph the line by locating the appropriate interce
pt, this your first coordinate. Then move to
your next coordinate using your slope.
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Use this same process and graph the second line.
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Once both lines have been graphed locate the
point of intersection for the lines. This point
is your solution set. In this example the
solution set is 2,2.
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In order to solve a system of equations
algebraically using addition first you must be
sure that both equation are in the same
chronological order.
Example
Could be
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Now select which of the two variables you want to
eliminate. For the example below I decided to
remove x.
The reason I chose to eliminate x is because
they are the additive inverse of each other.
That means they will cancel when added together.
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Now add the two equations together.
Your total is therefore
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Now substitute the known value into either one of
the original equations. I decided to substitute 3
in for y in the second equation.
Now state your solution set always remembering to
do so in alphabetical order.
-1,3
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Lets suppose for a moment that the equations are
in the same sequential order. However, you
notice that neither coefficients are additive
inverses of the other.
Identify the least common multiple of the
coefficient you chose to eliminate. So, the LCM
of 2 and 3 in this example would be 6.
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Multiply one or both equations by their
respective multiples. Be sure to choose numbers
that will result in additive inverses.
becomes
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Now add the two equations together.
becomes
Therefore
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Now substitute the known value into either one of
the original equations.
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Now state your solution set always remembering to
do so in alphabetical order.
-3,3
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In order to solve a system equations
algebraically using substitution you must have on
variable isolated in one of the equations. In
other words you will need to solve for y in terms
of x or solve for x in terms of y.
In this example it has been done for you in the
first equation.
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Now lets suppose for a moment that you are given
a set of equations like this..
Choosing to isolate y in the first equation the
result is
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Now substitute what y equals into the second
equation.
becomes
Better know as Therefore
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This concludes my presentation on simultaneous
equations. Please feel free to view it again at
your leisure.