Lineaarvõrrandisüsteemi
A linear equation system, also known as a system of linear equations, consists of two or more linear equations involving the same set of variables. The goal is to find the values of the variables that satisfy all the equations simultaneously. Linear equations are equations of the first degree, meaning the highest power of the variable is 1.
The general form of a system of linear equations with two variables x and y is:
where a1, b1, c1, a2, b2, and c2 are constants.
There are several methods to solve a system of linear equations, including:
1. Substitution method: Solve one equation for one variable and substitute it into the other equation.
2. Elimination method: Add or subtract the equations to eliminate one variable.
3. Matrix method: Use matrix operations to find the solution.
4. Graphical method: Plot the equations on a graph and find the intersection point.
The solution to a system of linear equations can be:
1. A unique solution: There is exactly one pair of values for x and y that satisfies
2. Infinitely many solutions: All pairs of values that satisfy one equation also satisfy the other.
3. No solution: There are no pairs of values that satisfy both equations.
The study of linear equation systems is fundamental in linear algebra and has applications in various