SOLUTION: 7X + 3Y = 14 , 5X + 9Y = 10 4X + Y = 16 , 2X + 3Y = 24 12X + Y = 25 , 8X - 2Y = 14

Notice the 3Y in the first equation and the 9Y
in the second equation.  If you multiply the
first equation by -3, the 3Y will become -9Y and
then if you add the two equations, the Y's will
cancel.  So let's multiply the first equation by
-3:



Simplifying:



Now we add corresponding terms.
-21X added to 5X gives -16X,
-9Y added to 9Y gives 0,
-42 added to 10 gives -32, so
by adding vertically term by 
term we have the equation:



Divide both sides by -16:



Now pick either one of the original
equations and substitute 2 for X:



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Notice the 4X in the first equation and the 2X
in the second equation.  If you multiply the
second equation by -2, the 2X will become -4X and
then if you add the two equations, the X's will
cancel.  So let's multiply the second equation by
-2:



Simplifying:



Now we add corresponding terms.
4X added to -4X gives 0,
Y added to -6Y gives -5Y,
16 added to -48 gives -32, so
by adding vertically term by 
term we have the equation:



Divide both sides by -5:




We could substitute this fraction in
for Y as we did in the previous problem.
However, unlike the previous problem,
 is difficult to subtitute.
So instead we will start over:



and this time we'll eliminate Y:

Notice the Y in the first equation and the 3Y
in the second equation.  If you multiply the
first equation by -3, the Y will become -3Y and
then if you add the two equations, the Y's will
cancel.  So let's multiply the first equation by
-3:



Simplifying:



Now we add corresponding terms.
-12X added to 2X gives -10X,
-3Y added to 3Y gives 0,
-48 added to 24 gives -24, so
by adding vertically term by 
term we have the equation:



Divide both sides by -16:

 



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You do this one by yourself.  It's just like the first one.

Answer: , 

Edwin