Introduction to Number Systems
ch1-introduction
Rational Numbers
ch1-rational-numbers
Exercise 1.1 - Detailed Solutions
ch1-exercise-1-1
Irrational Numbers
ch1-irrational-numbers
Exercise 1.2 - Detailed Solutions
ch1-exercise-1-2
Real Numbers & Decimal Expansions
ch1-real-decimals
Exercise 1.3 - Detailed Solutions
ch1-exercise-1-3
Operations on Real Numbers
ch1-operations
Rationalizing the Denominator
ch1-rationalization
Exercise 1.4 & 1.5 - Solutions
ch1-exercise-1-4-5
Laws of Exponents for Real Numbers
ch1-laws-exponents
Chapter 1 Summary
ch1-summary
What is a Polynomial?
ch2-introduction
Types of Polynomials
ch2-types
Zeroes of a Polynomial
ch2-zeroes
Exercise 2.1 - Detailed Solutions
ch2-exercise-2-1
Remainder Theorem
ch2-remainder-theorem
Factor Theorem
ch2-factor-theorem
Algebraic Identities
ch2-identities
Exercise 2.4 - Identity Applications
ch2-exercise-2-4
Chapter 2 Summary
ch2-summary
A solution is a pair (x,y) that satisfies the equation.
Check if (3,2) is a solution: 2(3)+3(2)=6+6=12 ✓
For 2x+3y=12:
| x | y | Solution |
|---|---|---|
| 0 | 4 | (0,4) |
| 3 | 2 | (3,2) |
| 6 | 0 | (6,0) |
A linear equation has infinitely many solutions!