>I have been working on this problem for about 3 hours now, and i have no clue how to solve it...
>
> x^2+ y^2=16
>4x +7y =13
Well, as you would approach many such problems, substitution is a good way to go if nothing tricky jumps out at you.
Solve one for a variable and substitute into the other.
4x + 7y = 13
Solve for x
4x = 13-7y
x = (1/4)�(13-7y)
x^{2} + y^{2} = 16
Substitute for x
[(1/4)�(13-7y)]^{2} + y^{2} = 16
Solve for y
(1/16)�(13-7y)^{2} + y^{2} = 16
(13-7y)^{2} + 16�y^{2} = 256
You take it from there. Simplify this equation and find a quadratic equation in y. You should get two solutions. (They had better be between 4 and -4. Do you see why?) Substitute each of these into either original equation to obtain the ordered pair associated with each solution.