3.5 Notes Part 1 - Solve Nonlinear Systems_Alg2

3.5 Notes Part 1 - Solve Nonlinear Systems

Solve the system using substitution:

x² = 2y + 10

3x - y = 9

• Solve equation 2 for y: y = 3x - 9

• Substitute equation 2 into equation 1: x² = 2(3x - 9) + 10

• Simplify: x² = 6x - 18 + 10 Simplify: x² = 6x - 8

• Write in standard form: x² - 6x + 8 = 0

• Factor: (x - 4)(x - 2) = 0

• Use zero product property: x - 4 = 0 or x - 2 = 0 Solve, x = 4 or x = 2

• Plug back into equation 2: y = 3(4) - 9 = 3 (4, 3) / y = 3(2) - 9 = -3 (2, -3)

Multiple Choice

Find the solution.

• (2,3) and (3,4)
• (-3,-15) and (4,-8)
• (-3,10) and (8,4)
• (-8,3) and (-4,10)