Algebra Foundations: Variables & Equations
Algebra is the language of mathematics. Variables let us write general rules; equations let us find unknown values. Master these foundations before everything that follows.
Key Concepts
Variables & Expressions
A variable (x, y, a) is a placeholder for a number. An expression like 3x + 5 doesn't have an equals sign. An equation like 3x + 5 = 17 does — and has a solution.
Solving Linear Equations
Goal: isolate the variable. 3x + 5 = 17 → subtract 5 → 3x = 12 → divide by 3 → x = 4. Each step applies the same operation to both sides.
Systems of Two Equations
Two equations, two unknowns: x + y = 10, x − y = 2. Solve by substitution or elimination. Adding both equations: 2x = 12 → x = 6, then y = 4.
Graphical Interpretation
A linear equation ax + by = c is a line. A system of two linear equations is where two lines intersect. No solution = parallel lines. Infinite solutions = same line.
Live Python Practice
Interactive Lab
Eq 2: x + y =
Check Your Understanding
To solve 4x − 3 = 13, the first step is to:
A system of two linear equations with no solution means:
In the system x + y = 5, x − y = 1, the solution is: