It depends on the system. There can be many, even infinitely many, depending on the system. For example, consider cos(x)=1, sin(x)=0; any multiple of 2*pi satisfies this system.
A system of equations may have any amount of solutions. If the equations are linear, the system will have either no solution, one solution, or an infinite number of solutions. If the equations are linear AND there are as many equations as variables, AND they are independent, the system will have exactly one solution.
1
A set of equations is inconsistent, if its solution set is empty.
dependent
No, a system of two linear equations cannot have exactly two solutions. In a two-dimensional space, two linear equations can either intersect at one point (one solution), be parallel (no solutions), or be the same line (infinitely many solutions). Therefore, it is impossible for a system of two linear equations to have exactly two solutions.
A system of equations may have any amount of solutions. If the equations are linear, the system will have either no solution, one solution, or an infinite number of solutions. If the equations are linear AND there are as many equations as variables, AND they are independent, the system will have exactly one solution.
A system of linear equations can only have: no solution, one solution, or infinitely many solutions.
As there is no system of equations shown, there are zero solutions.
In linear algebra, Cramer's rule is an explicit formula for the solution of a system of linear equations with as many equations as unknowns, valid whenever the system has a unique solution.
1
A set of equations is inconsistent, if its solution set is empty.
dependent
No, a system of two linear equations cannot have exactly two solutions. In a two-dimensional space, two linear equations can either intersect at one point (one solution), be parallel (no solutions), or be the same line (infinitely many solutions). Therefore, it is impossible for a system of two linear equations to have exactly two solutions.
If a system of linear equations has infinitely many solutions, it means that the two lines represented by the equations are coincident, meaning they lie on top of each other. This occurs when both equations represent the same line, indicating they have the same slope and y-intercept. As a result, any point on the line is a solution to the system.
A linear equation in n variables, x1, x2, ..., xn is an equation of the forma1x1 + a2x2 + ... + anxn = y where the ai are constants.A system of linear equations is a set of m linear equations in n unknown variables. There need not be any relationship between m and n. The system may have none, one or many solutions.
None, one or infinitely many.
There are three kinds:the equations have a unique solutionthe equations have no solutionthe equations have infinitely many solutions.