+1072 Find k if the system
has exactly one solution in real numbers.
+23252 The original equation (the absolute value equation) can be graphed in parts:
If x <= -23, then the equation is: y = -(x + 23) - (x - 5) - (x - 48) = -3x + 30
If -23 <= x < = 5, the equation is: y = (x _ 23) - (x - 5) - (x - 48) = -x + 76
If 5 <= x <= 48, the equation is: y = (x + 23) + (x - 5) - (x - 48) = x + 66
if x >= 58, then the equation is: y = (x + 23) + (x - 5) + (x - 48) = 3x - 30
If you graph these, you will see that a line with a slope of 2 will intersect this graph in one point only if the
point is the intersection of the two parts: y = x + 66 and y = 3x - 30 which occurs at (48, 114).
For y = 2x + k ---> 114 = 2(48) + k ---> k = 18.
