879 9.1 Systems of Linear Equations Step 4 Solve the system. To eliminate y, add the two equations. x + y = 107,527 (1) x - y = 6733 (2) 2x = 114,260 Add. x = 57,130 Solve for x. To find y, substitute 57,130 for x in equation (2). x - y = 6733 (2) 57,130 - y = 6733 Let x = 57,130. -y = -50,397 Subtract 57,130. y = 50,397 Multiply by -1. Step 5 State the answer. The median salary for the position of Accountant I was $57,130 in San Diego and $50,397 in Salt Lake City. Step 6 Check. The average of $57,130 and $50,397 is $57,130 + $50,397 2 = $53,763.50. Also, $57,130 - $50,397 = $6733, as required. S Now Try Exercise 101. Linear Systems with Three Unknowns (Variables) We have seen that the graph of a linear equation in two unknowns is a straight line. The graph of a linear equation in three unknowns requires a three-dimensional coordinate system. The three number lines, usually labeled x, y, and z, are placed at right angles. The graph of a linear equation in three unknowns is a plane. Some possible intersections of planes representing three equations in three variables are shown in Figure 6. A single solution (a) P I II III Points of a line in common I II III (b) Points of a line in common III I, II (c) All points in common I, II, III (d) III II I No points in common (e) No points in common III I II (f) I II III No points in common (g) No points in common III I, II (h) Figure 6
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