Does anyone know what this is?

Turn them into linear equation.
4y + x = -17
-x -x
4y = -x - 17
--- ---- ---
4 4 4
y = -1/4x - 17/4
-2y + 2x = 16
-2x -2x
-2y = -2x + 16
----- ---- -----
-2 -2 -2
y = 1x - 8
Solve for x.
-1/4x - 17/4 = 1x - 8
+1/4x +1/4x
-17/4 = 5/4x - 8
+8 +8
15/4 = 5/4x
------ -----
5/4 5/4
3 = x
Check:
-1/4(3) - 17/4 = 1(3) - 8
-3/4 - 17/4 = 3 - 8
-5 = -5