SOLUTION: <pre>Solve this system of equations 18x - 7y = 121 6x - 14y = 122</pre>

You can make the x's cancel, by multiplying
every term of the second one by -3, for then
the 6x on the bottom equation will become a
-18x and that will cancel with the 18x in the
first equation.  So we multiply every term of

 6x - 14y = 122

by -3, and that makes it become

-18x + 42y = -366

Now write that under the original first equation:

 18x -  7y =  121
-18x + 42y = -366

draw a line underneath and add equals to
equals:

 18x -  7y =  121
-18x + 42y = -366
-----------------
  0x + 35y = -245
 
Drop the 0x

       35y = -245

Divide both sides by 35

         y = -7

So that's the answer for y.

Next we start all over again and make the
y's cancel:

18x -  7y = 121
 6x - 14y = 122

You can make the y's cancel, by multiplying
every term of the first one by -2, for then
the -7y in the top equation will become a
+14y and that will cancel with the -14y in the
bottom equation.  So we multiply every term of

 18x -  7y = 121

by -2, and that makes it become

-36x + 14y = -242

Now write that above the original bottom equation:


-36x + 14y = -242
  6x - 14y =  122

draw a line underneath and add equals to
equals:

-36x + 14y = -242
  6x - 14y =  122
-----------------
-30x +  0y = -120
 
Drop the 0y

      -30x = -120

Divide both sides by -30

         y = 4
 
So the answer is

(x,y) = (-7,4)

When you graph the two lines,

18x -  7y = 121
 6x - 14y = 122



Now draw a vertical line from the point where they intersect 
directly upward to the x-axis:



Notice that it ends right at 4 on the x-axis,

so that checks with x = 4

Now draw a horizontal line from the point where they intersect 
directly leftward to the y-axis:



Notice that it ends right at -7 on the y-axis,

and that checks with y = -7

Edwin