Draw a line underneath:

3x-2y=10 
5x+2y= 6
--------

Add the red 3x to the red 5x.  That gives 8x.  Write that down below the line.

3x-2y=10 
5x+2y= 6
--------
8x

Add the green -2y to the green +2y.  But they just cancel out because they are
just alike except one has a - before it and the other has a +
before it:


3x-2y=10 
5x+2y= 6
--------
8x

Next bring down the equal sign

3x-2y=10 
5x+2y= 6
--------
8x   =

Now add the 10 and the 6 getting 16. Write that down:

3x-2y=10 
5x+2y= 6
--------
8x   =16

Now you have the equation



Divide both sides by 8:





x = 2

Go back to one of the original equations:

3x-2y=10

In place of x, substitute (2)

3(2)-2y=10

Multiply the 3 by the 2 getting 6

   6-2y=10

Add -6 to both sides:

   6-2y=10
  -6    -6
  --------
    -2y= 4

Now we have the equation:



We divide both sides by -2





y = -2

So the solution is (x,y) = (2,-2)

To check we substitute (2) for x and (-2) for y in each equation

     3x-2y=10 and      5x+2y=6
3(2)-2(-2)=10 and 5(2)+2(-2)=6
       6+4=10 and       10-4=6
        10=10 and          6=6

So the solution is correct.

Edwin