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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.

 Jun 20, 2023
 #1
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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.

 Jun 20, 2023
 #2
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This might help:

 

 Jun 20, 2023
 #3
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 Jun 20, 2023

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