SOLUTION: Given the system of equations {{{system(x-4y=-12,y=-4+2x)}}} Solve the system of equations by graphing.

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: Given the system of equations {{{system(x-4y=-12,y=-4+2x)}}} Solve the system of equations by graphing.      Log On


   

Question 172786: Given the system of equations


system%28x-4y=-12%2Cy=-4%2B2x%29


Solve the system of equations by graphing.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

First let's graph x-4y=-12.


In order to graph x-4y=-12, we need to solve for "y"


x-4y=-12 Start with the given equation.


-4y=-12-x Subtract x from both sides.


-4y=-x-12 Rearrange the terms.


y=%28-x-12%29%2F%28-4%29 Divide both sides by -4 to isolate y.


y=%28%28-1%29%2F%28-4%29%29x%2B%28-12%29%2F%28-4%29 Break up the fraction.


y=%281%2F4%29x%2B3 Reduce.




Looking at y=%281%2F4%29x%2B3 we can see that the equation is in slope-intercept form y=mx%2Bb where the slope is m=1%2F4 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%2F4, this means:

rise%2Frun=1%2F4


which shows us that the rise is 1 and the run is 4. This means that to go from point to point, we can go up 1 and over 4



So starting at , go up 1 unit


and to the right 4 units to get to the next point



Now draw a line through these points to graph y=%281%2F4%29x%2B3

So this is the graph of y=%281%2F4%29x%2B3 through the points and


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Now let's graph y=-4%2B2x


y=-4%2B2x Start with the given equation


y=2x-4 Rearrange the terms.




Looking at y=2x-4 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=-4


Since b=-4 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-4

So this is the graph of y=2x-4 through the points and


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

Graph of y=%281%2F4%29x%2B3 (red) and graph of y=2x-4 (green)

From the graph, we can see that the two lines intersect at the point (4,4). So the solution is (4,4)