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Key Concepts

Linear Equations

Linear equations are mathematical statements that express the equality of two linear expressions. They typically take the form ax + b = c, where a, b, and c are constants, and x is the variable. Solving these equations involves isolating the variable to find its value, which represents the point where the two sides of the equation are equal.

Isolating the Variable

Isolating the variable is a fundamental technique in solving equations, where the goal is to manipulate the equation to get the variable on one side and the constants on the other. This often involves performing inverse operations, such as addition, subtraction, multiplication, or division, to both sides of the equation to maintain equality. Mastery of this concept is crucial for effectively solving linear equations.

Substitution

Substitution is a method used in solving equations where one variable is replaced with an equivalent expression. In the context of linear equations, once the variable is isolated, its value can be substituted back into the original equation or other related equations to find additional unknowns. This technique is essential for solving systems of equations or verifying solutions.