In Exercises 19–28, solve each system by the addition method. x^2+y^2=13,x^2−y^2=5

Key Concepts

Systems of Equations

A system of equations consists of two or more equations with the same variables. The goal is to find the values of the variables that satisfy all equations simultaneously. In this case, we have a system involving two equations in terms of x and y, which can be solved using various methods, including substitution, elimination, or the addition method.

Addition Method (Elimination Method)

The addition method, also known as the elimination method, is a technique used to solve systems of equations by adding or subtracting the equations to eliminate one variable. This method is particularly useful when the equations are structured in a way that allows for easy cancellation of terms, leading to a simpler equation that can be solved for one variable.

Quadratic Equations

Quadratic equations are polynomial equations of degree two, typically in the form ax^2 + bx + c = 0. In the given system, the equations involve x^2 and y^2, which indicates that the solutions may involve quadratic relationships. Understanding how to manipulate and solve quadratic equations is essential for finding the values of x and y in this context.