SOLUTION: How do you solve the systems of linear equations using the graphing method? I understand the elimination method and etc., but I do not get how to solve using the graphing method.

Question 201739: How do you solve the systems of linear equations using the graphing method?
I understand the elimination method and etc., but I do not get how to solve using the graphing method.
I know that the first step is putting it in slope-intercept form, but the graphing part I am having trouble with. How do you graph it exactly? Is there a specific way to plot points?
For example, how do you solve for this:
4x+2y=8
y=-2x+6
So far I tried doing it, and I've gotten the answer (3,2) but I did it again and there was no solution because it was parrallel.
Found 2 solutions by stanbon, jim_thompson5910:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
4x+2y=8
y=-2x+6
----------------
Plot two points for each equation:
For 4x + 2y = 8
Let x = 0, then y = 4 giving you point (0,4)
Let x = 1, then y = 2 giving you point (1,2)
Plot those two points and draw a line thru them to get:

------------------------------------
For y = -2x + 6
Let x = 0, then y = 6 giving you point (0,6)
Let x = 1, then y = 4 giving you point (1,4)
Plot those two points and draw a line thru them to get:

-----------------
Estimate the point of intersection as best you can.
Check it in the two equations.
=========================================
Ans: There is no intersection as the two lines have the
same slope and have different y-intercepts.
=========================================
Cheers,
Stan H.
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Step 1: Graph

Start with the given 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 -2 and the run is 1. This means that to go from point to point, we can go down 2 and over 1

So starting at , go down 2 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 (which is also ) through the points and

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

Step 2: Graph

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 -2 and the run is 1. This means that to go from point to point, we can go down 2 and over 1

So starting at , go down 2 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

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

Step 3: Graph the two equations together on the same coordinate plane

Graph of (red) and (green).

From the graph, we can see that the two lines are parallel and will NEVER cross.

So this means that there are no solutions.

So the system is inconsistent.
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