Solving a System of Linear Equations with Three Variables
This page demonstrates the process of solving a system of linear equations with three variables using the triangle system method. The problem involves finding the coefficients of a quadratic function fx = ax² + bx + c, given three equations.
The solution process is as follows:
-
The initial system of equations is presented:
a + b + c = 15
3a - b = 15
12a = 48
-
The triangle system method is applied to solve for the variables a, b, and c.
-
The solution steps are shown in detail, including algebraic manipulations and substitutions.
-
The final values for a, b, and c are determined:
a = 4
b = -27
c = -16
-
The resulting quadratic function is presented: fx = 4x² - 27x - 16
Vocabulary: Triangle system Dreieckssystem - A method for solving systems of linear equations by transforming them into a triangular form.
Example: The system of equations is solved step-by-step, demonstrating how to use the triangle system method to find the values of a, b, and c.
Highlight: The final quadratic function fx = 4x² - 27x - 16 is obtained by substituting the solved values of a, b, and c into the general form ax² + bx + c.
Definition: A system of linear equations with three variables is a set of equations involving three unknown quantities, typically represented by letters such as x, y, and z or, in this case, a, b, and c.
This detailed solution provides a clear example of how to solve Gleichungssysteme mit 3 Variablen systemsofequationswith3variables and can be useful for students learning about lineare Gleichungssysteme lösen solvinglinearsystemsofequations.
