SOLUTION: Could someone please help me with a systems of equations problem? This one is using the graphing method to solve it. Also, when drawing the lines on the graph, could you please dra

Algebra ->  Graphs -> SOLUTION: Could someone please help me with a systems of equations problem? This one is using the graphing method to solve it. Also, when drawing the lines on the graph, could you please dra      Log On


   

Question 145294: Could someone please help me with a systems of equations problem? This one is using the graphing method to solve it. Also, when drawing the lines on the graph, could you please draw the dots too,because that shows me how to line it up so I can draw the lines right.I have a hard time with this.Thank you in advance for all your help,and time.
3x + y = -6
x + y = -4
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

Let's graph the first equation 3x+%2B+y+=+-6. To do this, we must first solve for y



3x%2By=-6 Start with the first equation


y=-6-3x Subtract 3+x from both sides


y=-3x-6 Rearrange the equation




Looking at y=-3x-6 we can see that the equation is in slope-intercept form y=mx%2Bb where the slope is m=-3 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 -3, this means:

rise%2Frun=-3%2F1


which shows us that the rise is -3 and the run is 1. This means that to go from point to point, we can go down 3 and over 1



So starting at , go down 3 units


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



Now draw a line through these points to graph y=-3x-6

So this is the graph of y=-3x-6 through the points and


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Let's graph the second equation x+%2B+y+=+-4+. To do this, we must first solve for y


x%2By=-4 Start with the second equation


y=-4-x Subtract +x from both sides


y=-x-4 Rearrange the equation





Looking at y=-x-4 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=-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 -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-4

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



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Graph of y=-3x-6 (red) and y=-x-4 (green)


So from the graph, we can see that the two lines intersect at the point (-1,-3).