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Linear Equation In Two Variables

A linear equation in two variables is an algebraic equation that can be written in the form ax + by + c = 0, where a, b, and c are real numbers, and a and b are not both zero. Geometrically, it always represents a straight line on a Cartesian plane.

Key Concepts

The highest power or degree of both variables in the equation is exactly one.

Every solution (x, y) of the equation corresponds to a specific point on the straight line representing the equation.

A single linear equation in two variables has infinitely many solutions because a line consists of infinite points.

Formula & Equation

ax + by + c = 0

x and y are the variables, a and b are the non-zero coefficients of x and y respectively, and c is the constant term.

Common Misconceptions

Myth: A single linear equation in two variables has only one unique solution.

Fact: A single linear equation in two variables actually has infinitely many solutions. A unique solution only exists when you solve a specific pair of intersecting linear equations.

Real World Applications

Calculating the total cost of purchasing two different items, such as buying 3 pens and 5 notebooks for a total of 150 rupees, represented as 3x + 5y = 150.

Expressing the relationship between a fixed monthly salary and a variable commission earned per sale to calculate total monthly income.

Frequently Asked Questions

What is the standard form of a linear equation in two variables?

The standard form is ax + by + c = 0, where a, b, and c are real numbers, and both a and b cannot be zero simultaneously.

How do you find the solution to a linear equation in two variables?

You can find a solution by assuming any real value for one variable, substituting it into the equation, and solving for the corresponding value of the other variable.

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