SOLUTION: solve the system by graghinng. then classify the system as consisten or inconsistent and as dependent or independent. y=2x-5 y=x-6 what is the solutionof the system of equat

Question 189578: solve the system by graghinng. then classify the system as consisten or inconsistent and as dependent or independent.
y=2x-5
y=x-6
what is the solutionof the system of equations?

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
First, let's graph

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

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

Now let's graph

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 on the same coordinate plane:

Graph of (red) and (green)

From the graph, we can see that the two lines intersect at the point (-1,-7)

So the solutions are and .

So the system is consistent and independent.
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