Two cases must be distinguished for the solutions of the equation ax+b=0: If a=0, then the equation either has no solutions (if b≠0) or it has infinitely many solutions (if b =0). So uniqueness really only exists if a≠0.
What does it mean when a solution is unique?
By the term unique solution we mean that for a given equation there is only one set of specific solutions. … So if we have two equations, then the unique solution means that there is one and only one point where the two equations intersect. 05
What is a single solution example?
The existence of a unique solution For example, if in a set of simultaneous linear equations with two equations and two unknowns, one equation x+y=2 x + y = 2 and another equation 3x+3y=5 3x + 3y = is 5, are these two equations are inconsistent in the given system.
How do you show that a differential equation has a unique solution?
By the term unique solution we mean that for a given equation there is only one set of specific solutions. … So if we have two equations, then the unique solution means that there is one and only one point where the two equations intersect. 05
What does one size mean?
By the term unique solution we mean that for a given equation there is only one set of specific solutions. … So if we have two equations, then the unique solution means that there is one and only one point where the two equations intersect.
How do you know if a solution is unique?
In a set of linear simultaneous equations, a unique solution exists if and only if (a) the number of unknowns and the number of equations are equal, (b) all equations are consistent, and (c) there is n linear dependence between two or more equations , i.e. all equations are independent.
What does it mean when a function is unique?
To say that a function that satisfies certain conditions is unique means that it is the only function that satisfies those conditions. For example, there is a unique function, y(x), that satisfies y= y, y(0)= 0, y(1)= 1. (This unique function is y(x)= sin(x).) Mathematics .
What does unique solution differential equation mean?
There is nothing better than “a unique solution to the differential equation”. “A problem *** has a unique solution” means that problem *** has a solution and problem *** has no other solution. “*** has a solution” means that “the problem *** has at least one solution”.
What is a one-size-fits-all solution?
By the term unique solution we mean that for a given equation there is only one set of specific solutions. … So if we have two equations, then the unique solution means that there is one and only one point where the two equations intersect.
How do I identify a unique solution?
Condition for a unique solution of linear equations A system of linear equations ax + by + c = 0 and dx + ey + g = 0 will have a unique solution if the two straight lines represented by the equations ax + by + c = 0 and dx + ey + g = 0 intersect in one point. that is, when the two lines are neither parallel nor coincident.
What is a unique solution in a matrix?
A system has a unique solution if it is consistent and the number of variables equals the number of non-zero rows. If the system matrix is rref, the solution is the single point ( 2, 1, 3 ) or x=2, y=1, z=3.
What is a Unique Class 9 Solution?
Note: The meaning of a unique solution is that the two lines we are talking about intersect or meet at a single point, giving a unique or one-to-one solution. … Parallel lines lead to no solution, while coincident lines refer to an infinity of solutions.