Algebra: Complete Notes, Formulas, Examples, and Practice Questions
Algebra: Complete Notes, Formulas, Examples, and Practice Questions 1. Linear Equations A. What is a Linear Equation? An equation of the form a x + b = 0 a x + b = 0 or a x + b y + c = 0 a x + b y + c = 0 , where a , b , c a , b , c are constants and x , y x , y are variables. B. How to Solve Isolate the variable on one side. For two variables, use substitution or elimination methods. Example 1: Solve for x x : 2 x + 22 = x + 1 2 x + 22 = x + 1 2 x + 22 = x + 1 2 x + 22 = x + 1 2 x − x = 1 − 22 2 x − x = 1 − 22 x = − 21 x = − 21 2 Example 2: Solve the system: 2 x + y = 8 2 x + y = 8 3 y = 4 + 4 x 3 y = 4 + 4 x Rewrite: 4 x − 3 y = − 4 4 x − 3 y = − 4 Solve simultaneously: x = 2 , y = 4 x = 2 , y = 4 2 2. Quadratic Equations A. What is a Quadratic Equation? An equation of the form a x 2 + b x + c = 0 a x 2 + b x + c = 0 , where a ≠ 0 a = 0 . B. Quadratic Formula x = − b ± b 2 − 4 a c 2 a x = 2 a − b ± b 2 − 4 a c C...