+184 Find the sum of the x-coordinates of the solutions to the system of equations y=|x^2-6x+5| and y=\frac{29}{4}-x.
The system of equations is:
y = |x^2-6x+5| y = \frac{29}{4}-x
We can solve this system of equations by graphing the two equations and finding the points where the graphs intersect.
The graph of the equation y = |x^2-6x+5| is a parabola. The graph of the equation y = \frac{29}{4}-x is a line. The graphs intersect at three points. The x-coordinates of these three points are 1, 4, and 5. The sum of these three x-coordinates is 1+4+5 = 10.
Therefore, the sum of the x-coordinates of the solutions to the system of equations is 10.
