x/3+y/2=3/2 x/2+y/5=-1/2

x/3+y/2=3/2

x/2+y/5=-1/2

?? what is the solution of this ??

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First off, let's simplify things by multipling the first equation on both sides by the common denominator of the fractions..... (6). And let's do the same thing for the second equation for the common denominator of its fractions .........(10).

So we get

2x + 3y  = 9

5x + 2y =  -5

I know there's a solution to this...... (Don't ask me how I  know, I just do!)

If we take the first equation and multiply it on both sides by the "negative" of the coefficient on y in the second equation, (-2), we have

-4x - 6y = -18

Now, take the second equation and multiply it on both sides by the coefficient on y in the first equation, (3). This gives us

15x + 6y = -15

Now, i'm just going to add the first equation to the second...if we do this correctly, we get

11x = -33.........notice how the"y's" just went away!! And solving for, x, we have

x = -3 And putting this back into ANY of the equations will give us "y."

So, using our last equation....

15(-3) + 6y = -15  and

-45 + 6y = -15      add 45 to both sides

6y = 30   so.......y = 5

So x = -3 and y = 5

These are the correct answers.......but don'r just take my word for it........substitute the values back into ANY of the equations and see if they "work'.....(hint: they will)..........