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

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) (Show Source): You can put this solution on YOUR website!

Let's graph the first equation . To do this, we must first solve for y

Start with the first equation

Subtract from both sides

Rearrange the equation

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 -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

So this is the graph of through the points

and

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

Let's graph the second equation . To do this, we must first solve for y

Start with the second equation

Subtract from both sides

Rearrange the equation

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 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

So this is the graph of through the points

and

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

Graph of (red) and (green)

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

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