SOLUTION: Solve the sytem of equations by graphing. Then classify the system. x+y=15 x-y=3

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Question 199578: Solve the sytem of equations by graphing. Then classify the system.
x+y=15
x-y=3
Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!
Start with the given system of equations:





In order to graph these equations, we must solve for y first.


Let's graph the first equation:


Start with the first equation.


Subtract from both sides.


Rearrange the terms and simplify.



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 -1 and the run is 1. This means that to go from point to point, we can go down 1 and over 1



So starting at , go down 1 unit


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


------------------------------------------------------------------------------


Now let's graph the second equation:


Start with the second equation.


Subtract from both sides.


Divide both sides by to isolate .


Rearrange the terms and simplify.



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 1 and the run is 1. This means that to go from point to point, we can go up 1 and over 1



So starting at , go up 1 unit


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


------------------------------------------------------------------------------


Now let's graph the two equations together:


Graph of (red). Graph of (green)


From the graph, we can see that the two lines intersect at the point . So the solution to the system of equations is . This tells us that the system of equations is consistent and independent.

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