SOLUTION: Solve each system by graphing. 3x-2y=6 6x+ 2y=-12

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Question 78872: Solve each system by graphing.
3x-2y=6
6x+ 2y=-12
Answer by Edwin McCravy(20077) About Me  (Show Source):
You can put this solution on YOUR website!

Solve each system by graphing.

3x - 2y = 6
6x + 2y = -12

Let's graph the first line by finding two points:

Let the x coordinate of the point be 0, since 0
is the easiest number to substitute in any equation:

So substituting 0 for x in

  3x - 2y = 6
3(0) - 2y = 6
   0 - 2y = 6
      -2y = 6
        y = 6/(-2)
        y = -3

So one point, the y-intercept is (0, -3)

Now let the y coordinate of a point be 0, since 0
is the easiest number to substitute in any equation:

So substituting 0 for y in

  3x - 2y = 6
3x - 2(0) = 6
       3x = 6
        x = 6/3
        x = 2
        
So another point, the x-intercept, is (2, 0)

Plot those points and draw a line through them:

graph%28400%2C400%2C-4.5%2C4.5%2C-6%2C3%2C+%286-3x%29%2F%28-2%29%29 

6x + 2y = -12

Now let's graph the second line the same way, by
finding two points:

Let the x coordinate of the point be 0, since 0
is the easiest number to substitute in any equation:

So substituting 0 for x in

  6x + 2y = -12
6(0) + 2y = -12
   0 + 2y = -12
       2y = -12
        y = -12/2
        y = -6

So one point, the y-intercept is (0, -6)

Now let the y coordinate of a point be 0, since 0
is the easiest number to substitute in any equation:

So substituting 0 for y in

  6x + 2y = -12
6x + 2(0) = -12
       6x = -12
        x = -12/6
        x = -2
        
So another point, the x-intercept, is (-2, 0)

Plot those points on the same set of axes as
the first line and draw a line through them:

graph%28400%2C400%2C-4.5%2C4.5%2C-6%2C3%2C+%286-3x%29%2F%28-2%29%2C+%28-12-6x%29%2F2%29 

Now draw a horizontal line through the point where 
the two lines cross:

graph%28400%2C400%2C-4.5%2C4.5%2C-6%2C3%2C+%286-3x%29%2F%28-2%29%2C+%28-12-6x%29%2F2%2C-4%29

Now draw a vertical line through the point where 
the two lines cross:



Notice that the horizontal line crosses the y-axis at -4, so the
y-coordinate of the solution is y = -4

The vertical line crosses the x-axis at a point between -1 and 0,
and we can estimate that to be about 2/3 of the way from 0 to -1,
so that would make the x-coordinate of the solution be x = -2/3.

Now we check to see if we have the correct answer, by substituting
in both original equations:

Substituting (x,y) = (-2/3,-4) in the first equation

        3x - 2y = 6
3(-2/3) - 2(-4) = 6
       -6/3 + 8 = 6
         -2 + 8 = 6
              6 = 6

That checks. 


6x + 2y = -12


Substituting (x,y) = (-2/3,-4) in the second equation

        6x + 2y = -12
6(-2/3) + 2(-4) = -12
      -12/3 - 8 = -12
         -4 - 8 = -12
            -12 = -12

That checks, too.  So the solution

(x,y) = (-2/3,-4)

is correct.

Edwin