Can someone tell me how to solve this system of equations

if 3x+2y=17 and 4x-5y=15, what is xy? I don't see anything obvious to isolate, like I have in the past, so I don't know what to do?

You can always use elimination. (as long as it's linear :P)

3x+2y = 17
4x-5y = 15

Then multiply the top by 4 and the bottom by -3. So
12x + 8y = 68
-12x + 15y = -45

Add:
23y = 23

y=1.

Then plugging back into the first original equation:
3x+2 = 17
3x = 15

x=5.

Finally, to answer the question, xy=5*1 = 5.

If you graphed the first equation you would get a line, thus there are infinite possibilities for the values of x and y. The same is true for the second equation. However, there is only one x/y pair that will fit into both equations so they are both true (plugging the pair into the first equation will give the result of 17, plugging the pair into the second results in 15). If you graphed both of these on the same graph they would intersect at the point where the coordinate matches the x/y pair. If, for both equations, the value of x is the same and the value of y is the same, you can do something like this:

First, isolate y for both equations.

3x+2y=17
Subtract 3x.
2y=17-3x
Divide by 2.
y=(17-3x)/2

4x-5y=15
Subtract 4x.
-5y=15-4x
Divide by -5.
y=(15-4x)/(-5)

Now, since y=y, you set those two resulting equations equal to each other.

(17-3x)/2=(15-4x)/(-5)
Solve for x. Cross multiply.
30-8x=-85+15x
Add 85.
115-8x=15x
Add 8x.
115=23x
Divide by 23.
5=x
x=5

You now have an x value. To find the y value, plug the x value into any of the above equations that include x and y.

y=(17-3x)/2
Substitute 5 into x.
y=(17-3(5))/2
Multiply.
y=(17-15)/2
Subtract.
y=2/2
Divide.
y=1

The solution (or intersection) for the system of equations is (5, 1).

3x + 2y = 17
4x - 5y = 15

solve for y in first equation and we get

2y = 17 - 3x
y = 17/2 - 3/2x

sub 17/2 - 3/2x for y in equation 2 and we get

4x - 5(17/2 - 3/2x) = 15

4x - 85/2 + 15/2x = 15

8/2x + 15/2x = 30/2 + 85/2

23/2x = 115/2

x = 115/23

x = 5

sub 5 for x in one of the original eqautions and solve for y. let's choose equaiton 1 and we get

3(5) + 2y = 17

15 + 2y = 17

2y = 2

y = 1

so xy = (5)(1) = 5

Solve for x and then solve for y
Suppose they come to x = 3 and y = 5. (they don't. It's just the way I'm explaining it to you).

xy = 3 * 5 = 15

It's a bit of a trick question.