SOLUTION: 3x-2y=8 2x-3y=7 solve each of the following system of equations by graphing

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Question 79725: 3x-2y=8
2x-3y=7
solve each of the following system of equations by graphing
Found 2 solutions by checkley75, Edwin McCravy:
Answer by checkley75(3666) About Me  (Show Source):
You can put this solution on YOUR website!
3x-2y=8 or -2y=-3x+8 or y=-3x/-2+8/-2 or y=3x/2-4 (red line)
2x-3y=7 or -3y-2x+7 or y=-2x/-3+7/-3 or y=2x/3-7/3 (green line)
+graph%28+300%2C+200%2C+-6%2C+5%2C+-10%2C+10%2C+y+=+3x%2F2+-4%2C+y+=+2x%2F3+-7%2F3%29+ (graph 300x200 pixels, x from -6 to 5, y from -10 to 10, of TWO functions y = 3x/2 -4 and y = 2x/3 -7/3).

Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!

solve the following system of equations by graphing

3x - 2y = 8
2x - 3y = 7 

Make a table of points for each equationm:

In the first, I arbitrarily chooss -2 for x
and substitute:

   3x - 2y = 8
3(-2) - 2y = 8
   -6 - 2y = 8
       -2y = 14
         y = -7

So one point on the graph of the first equation
in (-2,-7)

I arbitrarily chooss 2 for y
and substitute:

   3x - 2y = 8
 3x - 2(2) = 8
    3x - 4 = 8
        3x = 12
         x = 4

So another point on the graph of the first equation
in (4,2)
 
I arbitrarily chooss 0 for x
and substitute:

   3x - 2y = 8
 3(0) - 2y = 8
    0 - 2y = 8
       -2x = 8
         x = -4

So a third point on the graph of the first equation
in (0,-4).

So plot those points, (-2,-7), (4,2), (0,-4)

and draw a line through them:

graph%28300%2C300%2C+-5%2C6%2C-8%2C3%2C-%288-3x%29%2F2%29

In the second equation, I arbitrarily chooss
-1 for x and substitute:

   2x - 3y = 7
2(-1) - 3y = 7
   -2 - 3y = 7
       -3y = 9
         y = -3

So one point on the graph of the second equation
in (-1,-3)

I arbitrarily chooss 1 for y
and substitute:

   2x - 3y = 7
 2x - 3(1) = 7
    2x - 3 = 7
        2x = 10
         x = 5

So another point on the graph of the second equation
in (5,1)
 
I arbitrarily chooss -4 for x
and substitute:

   2x - 3y = 7
2(-4) - 3y = 7
   -8 - 3y = 7
       -3x = 15
         x = -5

So a third point on the graph of the second equation
in (-4,-5).

So plot those points, (-1,-3), (5,1), (-4,-5)
on the same set of axes and draw a line through them:

graph%28300%2C300%2C+-5%2C6%2C-8%2C3%2C-%288-3x%29%2F2%2C+-%287-2x%29%2F3%29

Through the point where those two lines cross, draw
a vertical line:

graph%28206%2C300%2C+-5%2C6%2C-8%2C3%2C-%288-3x%29%2F2%2C+-%287-2x%29%2F3%2C+999%28x-2%29%29

Notice that the vertical line crosses the x-axis at
the value 2.  So the x value of the solution is 2.

Also through the point where those two lines cross, draw
a horizontal line:



Notice that the horizontal line crosses the y-axis at
the value -1.  So the y value of the solution is -1.

The solution is therefore (x, y) = (2, -1)

Now let's check to see if this is the correct solution
by substituting in BOTH equations:

Substituting in the first:

     3x - 2y = 8
3(2) - 2(-1) = 8
       6 + 2 = 8
           8 = 8

That checks:

Substituting in the second:

     2x - 3y = 7
2(2) - 3(-1) = 7
       4 + 3 = 7
           7 = 7

That checks, too. So 
we know that this is the
correct solution.

Edwin