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) About Me  (Show Source):
You can put this solution on YOUR website!
Start with the given system of equations:


system%28x%2By=15%2Cx-y=3%29


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


Let's graph the first equation:


x%2By=15 Start with the first equation.


y=15-x Subtract x from both sides.


y=-x%2B15 Rearrange the terms and simplify.



Looking at y=-x%2B15 we can see that the equation is in slope-intercept form y=mx%2Bb where the slope is m=-1 and the y-intercept is b=15


Since b=15 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
slope=rise%2Frun

Also, because the slope is -1, this means:

rise%2Frun=-1%2F1


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 y=-x%2B15

So this is the graph of y=-x%2B15 through the points and


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Now let's graph the second equation:


x-y=3 Start with the second equation.


-y=3-x Subtract x from both sides.


y=%283-x%29%2F%28-1%29 Divide both sides by -1 to isolate y.


y=x-3 Rearrange the terms and simplify.



Looking at y=x-3 we can see that the equation is in slope-intercept form y=mx%2Bb where the slope is m=1 and the y-intercept is b=-3


Since b=-3 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
slope=rise%2Frun

Also, because the slope is 1, this means:

rise%2Frun=1%2F1


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 y=x-3

So this is the graph of y=x-3 through the points and


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Now let's graph the two equations together:


Graph of y=-x%2B15 (red). Graph of y=x-3 (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.