Simultaneous equations are a set of two or more equations with multiple variables that must be solved simultaneously to find the values of the variables that satisfy all equations.
The purpose of solving simultaneous equations is to find the values of the variables that satisfy all equations. This is useful in many real-world applications, such as analyzing systems of linear equations in physics and engineering, or finding the intersection points of two graphs in mathematics.
There are several methods for solving simultaneous equations, including substitution, elimination, and graphing. Each method has its own advantages and may be more appropriate for different types of equations.
A system of equations has a unique solution if the number of equations is equal to the number of variables, and the equations are independent (i.e. they cannot be simplified to the same equation). This means there is only one set of values for the variables that satisfies all equations.
Yes, depending on the number of equations and variables, a system of simultaneous equations can have one, zero, or infinitely many solutions. When there are more variables than equations, there may be multiple solutions that satisfy the equations, making the system underdetermined.