Equation in two variables

Definition

An equation in two variables is a mathematical statement that relates two different quantities, typically represented as $x$ and $y$. These equations can be graphed on a coordinate plane showing the relationship between the variables.

5 Must Know Facts For Your Next Test

1. The solution to an equation in two variables is an ordered pair $(x, y)$ that satisfies the equation.
2. Graphing an equation in two variables results in a curve or line on the coordinate plane.
3. Linear equations in two variables form straight lines, while non-linear equations can form curves such as parabolas or circles.
4. The standard form of a linear equation in two variables is $Ax + By = C$, where $A$, $B$, and $C$ are constants.
5. Systems of equations involve multiple equations with the same set of variables and can be solved using methods such as substitution, elimination, or graphing.

Review Questions

• What is the graphical representation of a linear equation in two variables?
• How do you determine if an ordered pair is a solution to an equation in two variables?
• What are common methods for solving systems of equations involving two variables?

Related terms

Linear Equation: An equation that forms a straight line when graphed and can be written as $Ax + By = C$.

Ordered Pair: A pair of numbers $(x, y)$ used to locate a point on the coordinate plane.

Coordinate Plane: A two-dimensional surface formed by two perpendicular number lines called axes.