Let

Integrate by parts, taking
<em>u</em> = <em>x</em> ==> d<em>u</em> = d<em>x</em>
d<em>v</em> = sin<em>ᵐ </em>(<em>x</em>) d<em>x</em> ==> <em>v</em> = ∫ sin<em>ᵐ </em>(<em>x</em>) d<em>x</em>
so that

There is a well-known power reduction formula for this integral. If you want to derive it for yourself, consider the cases where <em>m</em> is even or where <em>m</em> is odd.
If <em>m</em> is even, then <em>m</em> = 2<em>k</em> for some integer <em>k</em>, and we have

Expand the binomial, then use the half-angle identity

as needed. The resulting integral can get messy for large <em>m</em> (or <em>k</em>).
If <em>m</em> is odd, then <em>m</em> = 2<em>k</em> + 1 for some integer <em>k</em>, and so

and then substitute <em>u</em> = cos(<em>x</em>) and d<em>u</em> = -sin(<em>x</em>) d<em>x</em>, so that

Expand the binomial, and so on.
1: Solve for either x or y in one of the equations. So x + y = -1 is y = -x -1
2: substitute the new equation in the opposite equation. So x - (-x - 1) = 7
3: distribute the negative. X + x + 1 = 7
4: combine like terms. 2x + 1 = 7
5: solve for x. Subtract 1 on both sides. 2x = 6
6: divide by 2 to get x by itself. X = 3
7: plug the new value of x into one of the ORIGINAL equations. 3 + y = -1
8: solve for y. Subtract 3 on both sides.
Y = -4
9: the solution is written as (x,y) so the solution would be (3, -4)
15 minus 9 is equal to 6 <span />