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10-10 Nonlinear Systems

10-10 Nonlinear Systems. Solve the following systems of equations. 1. y = -2x² + 3 y = x + 3. {. -b 2a. 0 2(-2). = = 0. There is 1 solution to this system, (0, 3). {. 2. y = 2x + 1 y = x² + 7x + 5. 2x + 1 = x² + 7x + 5 -2x – 1 - 2x – 1

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10-10 Nonlinear Systems

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  1. 10-10 Nonlinear Systems Solve the following systems of equations. 1. y = -2x² + 3 y = x + 3 { -b 2a 0 2(-2) = = 0 There is 1 solution to this system, (0, 3).

  2. { 2. y = 2x + 1 y = x² + 7x + 5 2x + 1 = x² + 7x + 5 -2x – 1 - 2x – 1 0 = x² + 5x + 4 y = 2x + 1 y = 2(-1) + 1 y = -2 + 1 y = -1 and y = 2x + 1 y = 2(-4) + 1 y = -8 + 1 y = -7 -b   b² - 4ac 2a x = Solutions (-1, -1) & (-4, -7) -5   5² - 4·1·4 2·1 x = -5   25 - 16 2 x = -5   9 2 -5  3 2 x = = -8 2 -2 2 x = = -1 & = -4 Check by graphing

  3. { 2. y = 2x + 1 y = x² + 7x + 5 -7 2(1) -b 2a = = -3.5

  4. { 3. y = .1x + 3 y = -x² + 10x - 27 .1x + 3 = -x² + 10x – 27 -.1x – 3 - .1x – 3 0 = -x² + 9.9x - 30 -b   b² - 4ac 2a x = -9.9  9.9² - 4(-1)(-30) 2(-1) x = No Solution -9.9  98.01 - 120 -2 x = -9.9  -21.99 -2 x = Can’t take the square root of a negative number.

  5. 4. The population of A town is 30,000 and has an annual growth rate of 1.7%. The population of Another town is 28,000 and has an annual growth rate of 2.5%. Approximately how many years will pass before the towns have equal populations? What will their populations be at that time, to the nearest thousand? 8yrs ≈ 34,000 { x x f(x) = 30,000(1.017) g(x) = 28,000(1.025) Use a graphing calcu- lator’s tracer to get a close estimation. According to the calculator, it appears to be approximately 8 years. So check the tables to get the closest answer. Diff. ≈ 700 ≈ 500 ≈ 200 ≈ -50 ≈ -300

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