SOLUTION: x - y = 10 x - y = -2 What is the ordered pair? Is the system consistent or inconsistent? Is it dependent or independent? Can someone also give me a break down of how to do th

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons  -> Linear Equations Lesson -> SOLUTION: x - y = 10 x - y = -2 What is the ordered pair? Is the system consistent or inconsistent? Is it dependent or independent? Can someone also give me a break down of how to do th      Log On


   

Question 201975: x - y = 10
x - y = -2
What is the ordered pair?
Is the system consistent or inconsistent?
Is it dependent or independent?
Can someone also give me a break down of how to do this because I am very confused! Thank you!: Solve the system of equations by graphing. Then classify the system.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Step 1: Graph x+-+y+=+10


x-y=10 Start with the given equation.


-y=10-x Subtract x from both sides.


-y=-x%2B10 Rearrange the terms.


y=%28-x%2B10%29%2F%28-1%29 Divide both sides by -1 to isolate y.


y=%28-x%29%2F%28-1%29%2B%2810%29%2F%28-1%29 Break up the fraction.


y=x-10 Reduce.


Looking at y=x-10 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=-10


Since b=-10 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-10

So this is the graph of y=x-10 (and x-y=10) through the points and


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Step 2: Graph x+-+y+=+-2


x-y=-2 Start with the given equation.


-y=-2-x Subtract x from both sides.


-y=-x-2 Rearrange the terms.


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


y=%28-x%29%2F%28-1%29%2B%28-2%29%2F%28-1%29 Break up the fraction.


y=x%2B2 Reduce.



Looking at y=x%2B2 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=2


Since b=2 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%2B2

So this is the graph of y=x%2B2 (and x-y=-2) through the points and

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

Step 3: Graph the two equations together:




Graph of x-y=10 (red) and x-y=-2 (green)


From the graph, we can see that the two lines are parallel. So they will NEVER cross.


This means that there are no solutions.


So the system is inconsistent.