Chapter 8 Systems of Equations

8.1 Solving Systems of Equations Graphically System of Linear-Quadratic Equations is a linear and quadratic equation that involve the same variables, and involves a line and a parabola. System of Quadratic-Quadratic Equations are two quadratic equations involving the same variables, and has two parabolas. Any ordered pair (x,y) that satisfies both equations in a system of linear-quadratic or quadratic-quadratic equations is a solution of the system. A system of linear-quadratic or quadratic-quadratic equations can have no real solution, one real solution or two real solutions.

8.2 Solving Systems of Equations Algebraically Solve the system of linear-quadratic equations algebraically and verify your solution. 3x + y = - 9 4x2 - x + y = - 9 Check: (0, - 9) Solve 1) for y: y = -3x – 9 Substitute 1) into 2) 4x2 - x + (-3x - 9) = -9 3(0) + (- 9) = - 9 4x2 - x - 3x - 9 = - 9 - 9 = - 9 ✓ 4x2 - 4x = 0 4(0)2 - (0) + (-9) = - 9 4x (x-1) = 0 - 9 = - 9 ✓ 4x = 0 x -1 = 0 x = 0 x = 1 Check: ( 1, - 12) When x = 0 y = - 3(0) - 9 3(1) + (-12) = - 9 y = - 9 - 9 = - 9 ✓ 4(1)2 - (1) + (12) = - 9 When x = 1 y = - 3(1) - 9 - 9 = - 9 ✓ y = - 12