   Chapter 15.9, Problem 7E

Chapter
Section
Textbook Problem

Find the image of the set S under the given transformation.7. S = {(u, v)|0 ≤ u ≤ 3, 0 ≤ v ≤ 2}; x = 2u + 3v, y = u – v

To determine

To find: The image R of the region S by using transformation.

Explanation

Given:

The region is S={(u,v)|0u3,0v2} and x=2u+3v and y=uv .

Calculation:

From the given conditions,

x=2u+3v (1)

y=uv (2)

Solving the equations (1) and (2) as follows,

Solve the equation, (1)+3(2) gives u=x+3y5 .

Solve the equation, (1)2(2) gives v=x2y5

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