yhtälöryhmä

Yhtälöryhmä, in English a system of equations, is a collection of two or more equations that share the same variables. The goal when working with a system of equations is to find values for the variables that satisfy all equations in the system simultaneously. If such a set of values exists, it is called a solution to the system.

Systems of equations can involve any number of variables, such as two variables (e.g., x and y), three variables (e.g., x, y, and z), or more. The equations themselves can be of various types, including linear equations, quadratic equations, or even more complex forms. The most common type encountered in introductory algebra is a system of linear equations.

There are several methods for solving yhtälöryhmä. For linear systems, common techniques include substitution, elimination (also known as addition), and graphical methods. Substitution involves solving one equation for one variable and substituting that expression into the other equation. Elimination involves manipulating the equations so that when added or subtracted, one variable cancels out. Graphically, the solution to a system of linear equations represents the point(s) of intersection of the lines represented by the equations.

The number of solutions for a system of equations can vary. A system can have a unique solution, no solution (if the equations are contradictory), or infinitely many solutions (if the equations are dependent and essentially represent the same relationship). The nature of the solutions depends on the properties of the equations within the system.