Product of X and y

Question

If X+y=7 and X-y=9, find the product of x and y.

Answer 1

Lillianah, this is easier than you think, I promise!

 

Since you mention substitution, let's do it this way. Let's "solve" the first equation for x. Subtracting y from both sides, we get...

 

x = 7 - y

 

Now, we can substitute this "value" of x for x in the 2nd equation...

 

7 - y - y = 9

       -2y = 2

           y = -1

 

Hey, we have what y actually equals! Put that back into either equation...

 

x + (-1) = 7

     x - 1 = 7

            x = 8

 

Hope this helps!

Answer 2

Hi Lillianah,

You can solve the system of equations by the addition method.

          x + y = 7

          x - y = 9

Adding column by column we get 2x = 16 and x = 8. Substitute the value of x = 8 into either of the original equations. For instance using the first equation  8 + y = 7. Therefore y = -1. The product of x and y would be (8)(-1) = -8.

Answer 3

by adding the two equations you get 2x = 16 so x = 8.

 

then y = 7 - x = -1.

 

Therefore xy = -8.

Answer 4

Just for grins, I came up with another solution.  This avoids solving for x and y.

 

xy = ((x+y)^2 - (x-y)^2))/4 = (7^2 - 9^2)/4 = (49-81)/4 = -8