SOLUTION: I need to solve tis by graphing and have done this ten times and still can not find the points to graph. 3x-2y=6 3x+2y=6 Could somebody please help me figure out how to graph

Question 173156: I need to solve tis by graphing and have done this ten times and still can not find the points to graph.
3x-2y=6
3x+2y=6
Could somebody please help me figure out how to graph this? Thank you in advance. Judy
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Start with the given system of equations:

Let's graph the first equation:

Start with the first equation.

Subtract from both sides.

Rearrange the terms.

Divide both sides by to isolate y.

Break up the fraction.

Reduce.

Now let's graph 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 2. This means that to go from point to point, we can go up 3 and over 2

So starting at

, go up 3 units

and to the right 2 units 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

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

Now let's graph the second equation:

Start with the second equation.

Subtract from both sides.

Rearrange the terms.

Divide both sides by to isolate y.

Break up the fraction.

Reduce.

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 2. This means that to go from point to point, we can go down 3 and over 2

So starting at

, go down 3 units

and to the right 2 units 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

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

Now let's graph the two equations together:

Graph of (red). Graph of (green)

From the graph, we can see that the two lines intersect at the point

.

So the solution to the system of equations is

.

This tells us that the system of equations is consistent and independent.

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