Solving for U & P in a Coordinate Change

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SUMMARY

The discussion focuses on solving for the variables U and P in the coordinate transformation formula z = U·x + P. Given the new coordinates of -13 as 12 and -7 as 6, a system of equations is established: -13U + P = 12 and -7U + P = 6. By solving these equations, U is determined to be -3 and P is calculated to be -27. Additionally, for a new coordinate of 11, the original coordinate is found to be -6.

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Assume that you are given a coordinate change on a line which changes the coordinate x to a new coordinate z given by the formula z=U⋅x+P where U,P are real numbers with U non zero. If the new coordinate of the point -13 is 12 and the new coordinate of the point -7 is 6 then we must have U= ? and P= ? . Moreover, for the same transformation, if the new coordinate is (11) then the original coordinate must have been ?
 
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You can use the given information to set up a system of equations:

$$-13U+P=12$$

$$-7U+P=6$$
 

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