By I. Miller

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Graph x 2y have a point in common? 4 14. Graph x 2y have a point in common? = and x = and 2x 33. Graphical Solution. - 2y 8 = 4y 8 = In Art. 32 it 0. 0. Do these lines Do these lines was stated that the graph of a linear equation in two unknowns, x and y, is a straight line. The equation of this line will be satisfied by any number x and y and these values will be the coordinates of the points on the graph. Now assume that we have a second linear equation and that of pairs of values for its graph is drawn using the same coordinate axes.

X - The graphs y + 1 = 0; of equations (1) +y- 2x (2) and (2) 7 are - in the point are = 3), (2, 2, y = (I) numbered (2) in Figure 16. x 0. 3 They (1) and intersect whose coordinates and consequently is the solution of the system. The graphs may lines and two equations equations have no Such equations are their solution. said to be incompatible or inconsistent. (See Ex. 13, Art. ) Again the graphs of two equa- Fio. 16. tions the lines have an common and their The two equations of be parallel lines.

2. 3. - 2* - 5, find/(l),/(3),/(-2). - s 2 + 3, find F(l), F (-a). Given F(x) = Given /(*) a; Given /(n) 4. If /(s) = - z8 n 3 * +n+2 n 1 s and F(z) n2 + fmd/(l),/(2),/(i). = 2s 2 - 4s - 5, find the quotients an d F(2) 28. Functional relations. TF/ienet/er related that one depends, for its value, there is said to exist on ^o variables are so the value of the other a functional relationbetween these two variables. many examples of functional relations in most every line of endeavor. However, it is possible to express only a few of these relations in the form of an algebraic equation.

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