Here are the essential concepts you must grasp in order to answer the question correctly.
Ordered Pairs
An ordered pair consists of two elements, typically represented as (x, y), where 'x' is the first element and 'y' is the second. In the context of algebra, ordered pairs are used to represent points on a Cartesian coordinate system, allowing us to visualize relationships between variables. For example, the ordered pair (4, -1) indicates that x equals 4 and y equals -1.
Recommended video:
Fundamental Counting Principle
Substitution Method
The substitution method involves replacing variables in an equation with specific values to determine if a given ordered pair satisfies the equation. By substituting the x and y values from the ordered pair into the equation, we can check if the left-hand side equals the right-hand side. This method is fundamental in verifying whether points lie on a line represented by an equation.
Recommended video:
Choosing a Method to Solve Quadratics
Linear Equations
Linear equations are mathematical statements that describe a straight line when graphed on a coordinate plane. They typically take the form y = mx + b, where 'm' is the slope and 'b' is the y-intercept. In the given question, the equations x + 2y = 2 and x - 2y = 6 are linear equations, and determining if the ordered pair satisfies these equations helps us understand the relationship between the variables.
Recommended video:
Categorizing Linear Equations