SOLUTION: solve the following systems of equations graphically. x+y=3 5x-y=-3

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Question 243567: solve the following systems of equations graphically.
x+y=3
5x-y=-3
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
x%2By=3 Start with the first equation.


y=3-x Subtract x from both sides.


y=-x%2B3 Rearrange the terms.


Looking at y=-x%2B3 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=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, 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 down 1 and over 1



So starting at , go down 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%2B3

So this is the graph of y=-x%2B3 through the points and

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5x-y=-3 Move onto the next equation.


-y=-3-5x Subtract 5x from both sides.


-y=-5x-3 Rearrange the terms.


y=%28-5x-3%29%2F%28-1%29 Divide both sides by -1 to isolate y.


y=%28%28-5%29%2F%28-1%29%29x%2B%28-3%29%2F%28-1%29 Break up the fraction.


y=5x%2B3 Reduce.


Looking at y=5x%2B3 we can see that the equation is in slope-intercept form y=mx%2Bb where the slope is m=5 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 5, this means:

rise%2Frun=5%2F1


which shows us that the rise is 5 and the run is 1. This means that to go from point to point, we can go up 5 and over 1



So starting at , go up 5 units


and to the right 1 unit to get to the next point



Now draw a line through these points to graph y=5x%2B3

So this is the graph of y=5x%2B3 through the points and


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


If we plot the two equations on the same coordinate axis, we get:




Graph of y=-x%2B3 (red) and y=5x%2B3 (green)


From the graph, we see that the two lines intersect at the point (0,3).


So the solution to the system


system%28x%2By=3%2C5x-y=-3%29 is (0,3). In other words, x=0 and y=3 are solutions.