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﻿53 Simultaneous Equations and Graphs Q2 11 Solve the following simultaneous equations by drawing graphs. Use values 0 x < 6. a) y = x y = 2x y = 9 - 2x y = x + 1 b) y = 2x + 1 g) x + y = 5 2y = 8 + x 2x - 1 =y c) y = 4 - 2x h) 2y = 3x x + y = 3 y = x + 1 d) y = 3 -x i) y = x - 3 3x+y=5 y + x = 7 e) 2x + y = 6 j) y = x + 1 y = 3x + 1 2x + y = 10 The diagram shows the graphs: y = x2 - x y x + 2 y = 8 y = -2x + 4 Use the graphs to find the solutions (to 1 d.p.) to: a) x2 — x = 0 b) x2 - x = 8 c) x2 - x - 8 = 0 d) x2 - x = x + 2 e) x2 - 2x - 2 = 0 f) x2 - x = -2x + 4 g) x2 + x - 4 = 0 h) -2x + 4 = x + 2 -3x + 2 = 0 These equations look a bit nasty, but they're just made up of the equations you've got graphs for. And you know how to do the rest of it, don't you... Complete this table for y = + 5: -y2 )(2 y -1/2 x2+5 -4 -3 -2 y 12 11 10 9 y x2 - =8 -1 0 2 3 4 Draw the graph y = 1 + 5. Use your graph to solve the following equations (to 1 d.p.): a) - x2 + 5 = 0 2 b) - + 8 = 0 c) - —2 x2 -x + 5 = 0 ... x SECTION THREE — ALGEBRA