An Introduction To Mathematics - With Applns to Science and by I. Miller

By I. Miller

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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.

Using have a point in common? What are its coordinates? Do these coor- + 12. dinates satisfy both equations? 4 13. 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.

That is, a e __ = bd b'd VI. To divide one fraction and then multiply. That a :- The by another, invert the -c = ad = ad b be c number reciprocal of a is reciprocal of a 20. Reduction of a is 1 m 1 Thus the divisor is, d b ac of -; a n is n divided by the number. m fraction to its lowest terms. Separate the numerator and the denominator into their prime factors and then cancel common factors by division. Reduce to QJ4 . Solution. its x2 - lowest terms, + 6x -+ 9 = ; - x2 9 (x 7 (x + 8)(s + 3)r = - 3) (a + 3) x x + 3-' - 3 AN INTRODUCTION TO MATHEMATICS 18 [CHAP.

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