Question 170001: This is a systems of equations question.
If the equation is:
2x+6=y
3x+4y=24
__________
Please solve by substitution, elimination, AND graphing. ( the same equation)
Thank you so very much.
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website!
Table of Contents:
Substitution
Elimination
Graphing
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Substitution:
Note: the first equation  is the same as 
 Start with the second equation
 Plug in
 Distribute.
 Combine like terms on the left side.
 Subtract  from both sides.
 Combine like terms on the right side.
 Divide both sides by  to isolate  .
 Reduce. So this is the first part of the answer.
Go back to the first equation
 Plug in .
 Multiply  and  to get .
 Combine like terms. This is the second part of the answer.
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Answer:
So the solutions are and
Which forms the ordered pair (0,6)
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Elimination:
Start with the first equation
 Subtract 6 from both sides
 Subtract "y" from both sides
Start with the given system of equations:
 Multiply the both sides of the first equation by 4.
 Distribute and multiply.
So we have the new system of equations:
Now add the equations together. You can do this by simply adding the two left sides and the two right sides separately like this:
 Group like terms.
 Combine like terms. Notice how the y terms cancel out.
Simplify.
Divide both sides by to isolate .
Reduce.
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Now go back to the first equation.
 Plug in .
 Multiply.
 Remove any zero terms.
 Divide both sides by  to isolate  .
Reduce.
So our answers are and .
Which form the ordered pair ) . Note: this is the same answer as before.
This means that the system is consistent and independent.
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Graphing:
Start with the first equation
Rearrange the equation
Looking at we can see that the equation is in slope-intercept form  where the slope is  and the y-intercept is 
Since this tells us that the y-intercept is .Remember the y-intercept is the point where the graph intersects with the y-axis
So we have one point
Now since the slope is comprised of the "rise" over the "run" this means
Also, because the slope is , this means:
which shows us that the rise is 2 and the run is 1. This means that to go from point to point, we can go up 2 and over 1
So starting at , go up 2 units
and to the right 1 unit to get to the next point )
Now draw a line through these points to graph
 So this is the graph of through the points and
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Now move onto the second equation
 Subtract  from both sides.
 Rearrange the terms.
 Divide both sides by  to isolate y.
 Break up the fraction.
 Reduce.
Looking at we can see that the equation is in slope-intercept form where the slope is  and the y-intercept is
Since this tells us that the y-intercept is .Remember the y-intercept is the point where the graph intersects with the y-axis
So we have one point
Now since the slope is comprised of the "rise" over the "run" this means
Also, because the slope is  , this means:
which shows us that the rise is -3 and the run is 4. This means that to go from point to point, we can go down 3 and over 4
So starting at , go down 3 units
and to the right 4 units to get to the next point )
Now draw a line through these points to graph
 So this is the graph of through the points and
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Now let's graph the two equations together on the same coordinate system:
 Graph of (red) and graph of (green)
Notice how the two lines intersect at the point (0,6). So this means that the solution is and (which confirms our previous answers)
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