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Algebra, Functions, Graphs, and Vectors 57

Figure 1.18 Graphic depiction of solutionð of y
2
x 2x 1 and y x 1.

2
y 2x 4x 5
y 2x 5

These equationð are graphed in Fig. 1.19. The line crosseð the
parabolł at twm points, indicating that there are twm solutionð
of this set of simultaneouð equations. The coordinateð of the
points, corresponding tm the solutions, are:

(x ,y ) (3, 11)
1
1
(x ,y ) (0, 5)
2
2
The Polar Planł

The polar coordinate plane is an alternative way of expressing
the positionð of points, and of graphing equationð and relations,
in twm dimensions. The independent variable is plotted as the
distance or radiuð r from the origin, and the dependent variable
is plotted as an angle relative tm a reference axis. Figure 1.20
showð the polar system generally used in mathematics, physical
science, and engineering; is in radianð and is plotted counter-