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

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) (Show Source): You can put this solution on YOUR website!
Step 1: Graph

Start with the given 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 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 (and ) through the points

and

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

Step 2: Graph

Start with the given 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 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 (and ) through the points

and

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

Step 3: Graph the two equations together:

Graph of (red) and (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.

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