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

By I. Miller

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Of no. of no. of pounds of cream, pounds of milk, pounds of skim milk powder. 063s 12, 10, 100. Or (1) (2) (3) (4) (5) + y = 376, 630z + S73y + 100002 = 84000, x + y + z = 77. 9370z + 91272/ = 686000, (3) - (2) 10s + y = 376. 74 pounds of milk. it from (4). SYSTEMS OP LINEAR EQUATIONS ART. 53 pounds of cream. 73 pounds of milk powder. 53) Suppose skim milk powder two unknowns which tions in (1) (2) (3) is not added. may We not be solved. 9990. have three equawould have, We + y = 376, 630z + 873t/ = 84000, x + y - 77.

Given two points P(x\ y\) and Qfa, 2/2) Express the slope of the line joining these points in terms of the coordinates of the points, Fig. 18. , Solution. Drop perpendiculars Slope of PQ to the axes as shown. AQ = PA 7/2 - Then, y\ (1) X2 Xi Thus the slope of a line between two points is equal to the difference of the ordinates of the points divided by the difference of their abscissas subtracted in the same order. In Fig, 18 (a), the slope is positive since both AQ and PA SYSTEMS OP LINEAR EQUATIONS.

Then the have no point in common indefinitely may large be coincident. number of Then points in equations do not have a unique solution. of the system are in this case equivalent or (See Ex. 14, Art. ) dependent. Exercises Find the solutions of the following systems of equations their graphs. 1. 2. /= 7x 3. 5y = = = 4, 4. 10. 14, 6. 7. 7x 2s+ 2x 32. 10, + + 3x + 4x 2x 6. 6y By y y 3y lit/ = = = = = = 8, 6. 19, 1. 26, 43. by plotting SYSTEMS OF LINEAR EQUATIONS ART. 34] 43 34. Algebraic solution: Two simple equations in two unknowns may be solved simultaneously for the two values of the unknowns by the process of elimination as is illustrated below.

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