Final answer:
The solution of the system involving the equations Y2 and Y3 is undefined as they represent parallel lines with the same slope but different y-intercepts. Hence, there is no ordered pair that represents the intersection of these lines.
Step-by-step explanation:
To estimate the solution of the system of equations, we are presented with two lines that share the same slope as a line of best fit. The equations presented are Y2 = -173.5 + 4.83x − 2(16.4), and Y3 = -173.5 + 4.83x + 2(16.4). It is mentioned that y = -173.5+ 4.83x is the line of best fit, which implies the slope remains identical for Y2 and Y3.
The equations provided for Y2 and Y3 include the line of best fit with adjustments made to the y-intercept. Specifically, for Y2 the y-intercept is reduced by 2(16.4), while for Y3 it is increased by the same amount. This suggests that Y2 and Y3 are parallel lines to the line of best fit, displaced vertically.
Solving the system of equations
To solve for the ordered pair that represents the intersection point of Y2 and Y3, we would typically set the two equations equal to each other and solve for x. However, since the slopes are identical and the y-intercepts are different, these lines will never intersect, making the solution undefined or nonexistent in the context of a Cartesian plane.
When confronted with a real-world scenario that involves parallel lines like this, it is often a sign to reassess the situation or understand that the lines represent different scenarios or boundaries that do not converge on a single point.