I'm not 100% certain about what you're asking, but each function and relation can have different solutions, either one of the three ways. (Always dealing with two equations) This is based off my Grade 10 Knowledge
One (Intersecting at one specific point)
None (Parallel Lines)
Coincident two lines with the same slope and intercept)
Refer back to : " y=mx+b " equation if needed.
If you are talking about the possible ways to find the solution (x,y), there are also three.
Elimination, (Removing one variable to solve the equation)
Substitution, (Knowing what x or y, and inputting in the second equation)
Graphing, (By drawing both equations, This method is not very accurate)
If a system of equations is inconsistent, there are no 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.
if a dependent system of equation is solved, how many solutions will there be?
The answers to equations are their solutions
The answer follows:
Systems of equations can have just about any number of solutions: zero, one, two, etc., or even infinitely many solutions.
One solution
If they are quadratic equations then if their discriminant is less than zero then they have no solutions
If a system of equations is inconsistent, there are no solutions.
As there is no system of equations shown, there are zero solutions.
Infinite simultaneous solutions. (The two equations represent the same line) OR If your in nova net the answer should be ( Many )
That means the same as solutions of other types of equations: a number that, when you replace the variable by that number, will make the equation true.Note that many trigonometric equations have infinitely many solutions. This is a result of the trigonometric functions being periodic.
A way to solve a system of equations by keeping track of the solutions of other systems of equations. See link for a more in depth answer.
Simultaneous equations have the same solutions.
2
Eduard Reithmeier has written: 'Periodic solutions of nonlinear dynamical systems' -- subject(s): Differentiable dynamical systems, Nonlinear Differential equations, Numerical solutions
Linear equations with one, zero, or infinite solutions. Fill in the blanks to form a linear equation with infinitely many solutions.