Algebra

Linear Equations

Standard form: y = mx + b

• m = slope (rise over run)
• b = y-intercept (where line crosses y-axis)
• Two points on a line: find slope first, then substitute to find b.

Systems of Equations

Two equations, two unknowns. Solve by:

• Substitution: solve one equation for x, substitute into the other.
• Elimination: add or subtract equations to cancel one variable.

Example: x + y = 10 and x − y = 4 → add: 2x = 14 → x = 7, y = 3.

Polynomials

• Combining like terms: 3x² + 2x − x² + 5 = 2x² + 2x + 5
• FOIL (multiply two binomials): (x+3)(x+2) = x² + 2x + 3x + 6 = x² + 5x + 6
• Factoring: x² + 5x + 6 = (x+2)(x+3)