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

Algebra ->  Linear-equations -> 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      Log On


   

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) About Me  (Show Source):
You can put this solution on YOUR website!
First, let's graph y=2x-5



Looking at y=2x-5 we can see that the equation is in slope-intercept form y=mx%2Bb where the slope is m=2 and the y-intercept is b=-5


Since b=-5 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 2, this means:

rise%2Frun=2%2F1


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 y=2x-5

So this is the graph of y=2x-5 through the points and



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Now let's graph y=x-6





Looking at y=x-6 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=-6


Since b=-6 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-6

So this is the graph of y=x-6 through the points and


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Now let's graph the two equations on the same coordinate plane:

Graph of y=2x-5 (red) and y=x-6 (green)


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


So the solutions are x=-1 and y=-7.


So the system is consistent and independent.