lightbulb Key Concepts

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1. Introduction to Linear Equations

A linear equation in one variable is an equation which can be written in the form ax + b = 0, where a and b are real numbers and a ≠ 0.

2. Linear Equations in Two Variables

The general form is ax + by + c = 0. The graph of such an equation is always a straight line.

• Slope-Intercept Form: y = mx + c (m is slope, c is y-intercept)
• Point-Slope Form: y - y₁ = m(x - x₁)
• Intercept Form: x/a + y/b = 1

3. Solving Systems of Linear Equations

• Substitution Method: Express one variable in terms of the other and substitute.
• Elimination Method: Multiply equations to make coefficients equal and add/subtract.
• Graphical Method: The point of intersection is the solution.