Let $a_1,$ $a_2,$ $a_3,$ $\dots,$ $a_{10},$ $a_{11},$ $a_{12}$ be an arithmetic sequence. If $a_1 + a_3 + a_5 = 22$ and $a_2 + a_4 = 17$, then find $a_1$.
a1 + a3 + a5 = 22
a1 + (a1 + d) + (a1 + 2d) =22
3a1 + 3d = 22
a2 + a4 = 17
(a1 + d) + (a1 + 3d) = 17
2a1 + 4d = 17
3a1 + 3d = 22 mult through by 4 → 12a1 + 12d = 88
2a1 + 4d = 17 mult through by -3 → -6a1 - 12d = -51 add these
6a1 = 37
a1 = 37 / 6
+782 
