1. Chapter 8 Systems of Equations

2. 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.

3. 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) = (0) + (- 9) = - 9
4x2 - x - 3x - 9 = = - 9 ✓
4x2 - 4x = (0)2 - (0) + (-9) = - 9
4x (x-1) = = - 9 ✓
4x = x -1 = 0
x = x = 1 Check: ( 1, - 12)
When x = 0 y = - 3(0) (1) + (-12) = - 9
y = = - 9 ✓
4(1)2 - (1) + (12) = - 9
When x = 1 y = - 3(1) = - 9 ✓
y = - 12