Find k if the system
\(\begin{align*} y &= |x + 23| + |x - 5| + |x - 48|, \\ y &= 2x + k \end{align*}\)
has exactly one solution in real numbers.
+33652 The graph below shows that the value of k must lie between 0 and 100. Clearly, you want the value of k that just clips the red graph at x = 50, so find the value of y on the red graph at x = 50 using the first equation, plug that into the second equation together with x = 50 and rearrange the resulting expression to find k.
Edit: The value of x = 50 is incorrect - see below.
Hi Alan, thanks for responding. I tried your method as follows:
Plugging x=50 into the first equation:
y= 73+45+2
y=120
Plugging x=50 and y=120 into the second equation and solving for k:
120=2(50) + k
k=20
I tried inputting this answer but it is saying my answer is wrong. I also don't understand where you got x=50 from.
+33652 Oops! I was careless in looking at the graph and misled myself (and you!). The point where the two functions meet at a single point is at x = 48, not 50. Plug this into the first function to get y (= 114). Then use this value of y in the second function, together with x = 48 to get k ( = 18).
