Solving Systems of Equations 3 Approaches Mrs. N. Newman Click here to begin.
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Transcript of Solving Systems of Equations 3 Approaches Mrs. N. Newman Click here to begin.
Solving Systems of Equations
3 Approaches
Mrs. N. NewmanClick here to begin
Method #1
Graphically
Method #2
Algebraically Using Addition and/or Subtraction
Method #3
Algebraically Using Substitution
Door #1
Door #2
Door #3
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.
bmxy
Graph the line by locating the appropriate
intercept, this your first coordinate. Then move to your next
coordinate using your slope.
Use this same process and graph the second line.
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].
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: 2
4
yx
xy
2
4
xy
xyCould be
Now select which of the two variables you want to eliminate.
For the example below I decided to remove x.
2
4
xy
xy
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.
Now add the two equations together.
2
4
xy
xy
Your total is:
therefore 3
62
y
y
Now substitute the known value into either one of the original equations.I decided to substitute 3 in for y in the second equation.
1
23
x
x
Now state your solution set always remembering to do so in alphabetical order.
[-1,3]
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.
1273
332
yx
yx
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.
Multiply one or both equations by their
respective multiples. Be sure to choose numbers that
will result in additive inverses.
)1273(2
)332(3
yx
yx
24146
996
yx
yxbecomes
Now add the two equations together.
24146
996
yx
yxbecomes 155 y
Therefore 3y
Now substitute the known value into either one of the original equations.
3
62
392
3)3(32
3
x
x
x
x
y
Now state your solution set always remembering to do so in alphabetical
order.
[-3,3]
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.
2
4
yx
xy
Now lets suppose for a moment that you are given a set of equations like this..
1273
332
yx
yx
Choosing to isolate y in the first equation the result is :
13
2 xy
Now substitute what y equals into the second equation.
2
4
yx
xy
becomes24 xx
Better know as
Therefore 1
22
242
x
x
x
This concludes my presentation on simultaneous equations.
Please feel free to view it again at your leisure.